Technical Reports

2022

RAL-TR-2022-004 (PDF(link opens in a new window))
J. Reid
The new features of Fortran 202x
RAL-TR-2022-002 (PDF(link opens in a new window))
M. O'Flynn, J. Fowkes, N. Gould
Global optimization of crystal field parameter fitting in Mantid

2020

RAL-P-2020-004 (PDF(link opens in a new window))
J. Scott and M. Tuma
A computational study of using black-box QR solvers for large-scale sparse-dense linear least squares problems
RAL-P-2020-003 (PDF(link opens in a new window))
J. Scott and M. Tuma
A null-space approach for symmetric saddle point systems with a non zero (2,2) block
RAL-P-2020-002 (PDF(link opens in a new window))
T. Rees and M. Wathen
An element-based preconditioner for mixed finite element problems
RAL-P-2020-001 (PDF(link opens in a new window))
C. Cartis, N.I.M. Gould, P.L. Toint
Strong evaluation comlexity bounds for arbitrary-order optimization of nonconvex nonsmooth composite functions

2019

RAL-TR-2019-005 (PDF(link opens in a new window))
C. Cartis, N.I.M. Gould, M. Lange
On monotonic estimates of the norm of the minimizers of regularized quadratic functions in Krylov spaces
RAL-TR-2019-004 (PDF(link opens in a new window))
N.I.M. Gould and V. Simoncini
Error estimates for iterative algorithms for minimizing regularized quadratic subproblems
RAL-TR-2019-003 (PDF(link opens in a new window))
T. Davis, I.S. Duff, S. Nakov
Design and implementation of a parallel Markowitz Threshod Algorithm
RAL-TR-2019-001 (PDF(link opens in a new window))
N.I.M. Gould, T. Rees and J.A. Scott
Convergence and evaluation-complexity analysis of a regularized tensor-Newton method for solving nonlinear least-squares problems subject to convex constraints
RAL-P-2019-004 (PDF(link opens in a new window))
I. Dauzickaite, A.S. Lawless, J.A. Scott, P.J. van Leeuwen
Spectral estimates for saddle point matrices arising in weak constraint four-dimensional variational data assimilation
RAL-P-2019-002 (PDF(link opens in a new window))
M. Wathen and C. Greif
A scalable approximate inverse block preconditioner for an incompressible magnetohydrodynamics model problem
RAL-P-2019-001 (PDF(link opens in a new window))
J.A. Scott and M. Tuma
Strengths and limitations of stretching for least-squares problems with some dense rows

2018

RAL-P-2018-012 (PDF(link opens in a new window))
I. Duff, J. Hogg, F. Lopez
A new sparse symmetric indefinite solver using a posteriori threshold pivoting
RAL-P-2018-006 (PDF(link opens in a new window))
C. Cartis, N.I.M. Gould, Ph.L. Toint
Sharp worst-case evaluation complexity bounds for arbitrary-order nonconvex optimization with inexpensive constraints
RAL-TR-2018-008 (PDF(link opens in a new window))
S. Cayrols, I.S. Duff and F. Lopez
Parallelization of the solve phase in a task-based Cholesky solver using a sequential task flow model
RAL-P-2018-004 (PDF(link opens in a new window))
I.S. Duff, P.A. Knight, L. le Gorrec, S. Mouysset and D. Ruiz
Uncovering hidden block structure
RAL-P-2018-002 (PDF(link opens in a new window))
J.A. Scott and M. Tuma
Sparse stretching for solving sparse-dense linear least-squares problems

2017

RAL-TR-2017-010 (PDF(link opens in a new window))
I.S. Duff, F. Lopez, S. Nakov
Sparse Direct Solution on Parallel Computers
RAL-P-2017-010 (PDF(link opens in a new window))
N.I.M. Gould, T. Rees, J.A. Scott
A higher order method for solving nonlinear least-squares problems
RAL-P-2017-009 (PDF(link opens in a new window))
N.I.M. Gould, T. Rees, J.A. Scott
Convergence and evaluation-complexity analysis of a regularized tensor-Newton method for solving nonlinear least-squares problems
RAL-P-2017-008 (PDF(link opens in a new window))
S. Lungten, W.H.A. Schilders and J.A. Scott
Preordering saddle-point systems for sparse LDLT factorization without pivoting
RAL-P-2017-007 (PDF(link opens in a new window))
C. Cartis, N.I.M. Gould, Ph.L. Toint
Worst-case evaluation complexity and optimality of second-order methods for nonconvex smooth optimization
RAL-TR-2017-006 (PDF(link opens in a new window))
I.S. Duff and F. Lopez
Experiments with sparse Cholesky using a parametrized task graph implementation
RAL-P-2017-006 (PDF(link opens in a new window))
C. Cartis, N.I.M. Gould, Ph.L. Toint
Improved second-order evaluation complexity for unconstrained nonlinear optimization using high-order regularized models
RAL-P-2017-005 (PDF(link opens in a new window))
C. Cartis, N.I.M. Gould, Ph.L. Toint
Optimality of orders one to three and beyond : characterization and evaluation complexity in constrained nonconvex optimization
RAL-TR-2017-003 (PDF(link opens in a new window))
I.S. Duff, A.M. Erisman, J.K. Reid
The Hellerman-Rarick algorithm
RAL-P-2017-002 (PDF(link opens in a new window))
J.A. Scott and M. Tuma
A Schur complement approach to preconditioning sparse linear least-squares problems with some dense rows
RAL-P-2017-003 (PDF(link opens in a new window))
F. Furini, E. Traversi, P. Belotti, A. Frangioni, A. Gleixner, N.I.M. Gould, L. Liberti, A. Lodi, R. Misener, H. Mittelmann, N.V. Sahinidis, S. Vigerske and A. Wiegele
QPLIB: A Library of Quadratic Programming Instances
RAL-P-2017-001 (PDF(link opens in a new window))
J.A. Scott and M. Tuma
Solving mixed sparse-dense linear least squares by preconditioned iterative methods

2016

RAL-P-2016-016 (PDF(link opens in a new window))
I.S. Duff, J. Hogg and F. Lopez
Experiments with sparse Cholesky using a sequential task-flow implementation
RAL-P-2016-010 (PDF(link opens in a new window))
C. Cartis, N.I.M. Gould and Ph.L. Toint
Universal regularization methods-varying the power, the smoothness and the accuracy
RAL-P-2016-009 (PDF(link opens in a new window))
J. Hogg, J. Hook, J.A. Scott and F. Tisseur
A max-plus approach to incomplete Cholesky factorization preconditioners
RAL-P-2016-008 (PDF(link opens in a new window))
C. Cartis, N.I.M. Gould and Ph.L. Toint
Second-order optimality and beyond: characterization and evaluation complexity in nonconvex convexly-constrained optimization
RAL-P-2016-006 (PDF(link opens in a new window))
E. Chow and J.A. Scott
On the use of iterative methods and blocking for solving sparse triangular systems in incomplete factorization preconditioning
RAL-P-2016-005 (PDF(link opens in a new window))
J.A. Scott
On using Cholesky-based factorizations for solving rank-deficient sparse linear least-squares problems
RAL-P-2016-004 (PDF(link opens in a new window))
J.D. Hogg, J.A. Scott and H.S. Thorne
Numerically-aware orderings for sparse symmetric linear systems
RAL-P-2016-003 (PDF(link opens in a new window))
N.I.M. Gould and D.P. Robinson
A dual gradient-projection method for large-scale strictly convex quadratic probems
RAL-P-2016-002 (PDF(link opens in a new window))
D. Packwood, J.R. Kermode, L. Mones, N. Bernstein, J Woolley, N.I.M. Gould, C. Ortner and G. Csanyi
A universal preconditioner for simulating condensed phase materials
RAL-P-2016-001 (PDF(link opens in a new window))
J.A. Scott and M. Tuma
Preconditioning of linear least squares by RIF for implicitly held normal equations

2015

RAL-TR-2015-011 (PDF(link opens in a new window))
C. Cartis, N.I.M. Gould and Ph.L. Toint
Improved worst-case evaluation complexity for potentially rank-deficient nonlinear least-Euclidean-norm problems using higher-order regularized models
RAL-P-2015-010 (PDF(link opens in a new window))
N.I.M. Gould and J.A. Scott
The state-of-the-art of preconditioners for sparse linear least-squares problems
RAL-TR-2015-010 (PDF(link opens in a new window))
C. Cartis, N.I.M. Gould and Ph.L. Toint
Evaluation complexity bounds for smooth constrained nonlinear optimization using scaled KKT conditions and high-order models
RAL-TR-2015-009 (PDF(link opens in a new window))
N.I.M. Gould and J.A. Scott
The state-of-the-art of preconditioners for sparse linear least-squares problems: the complete results
RAL-P-2015-005 (PDF(link opens in a new window))
P. Dunning, E. Ovtchinnikov, J.A. Scott and A. Kim
Level-set topology optimization with many linear buckling constraints using an efficient robust eigensolver
RAL-P-2015-004 (PDF(link opens in a new window))
N.I.M. Gould and J.A. Scott
A note on performance profiles for benchmarking software
RAL-P-2015-002 (PDF(link opens in a new window))
J.A. Scott and M. Tuma
Solving symmetric indefinite systems using memory efficient incomplete factorization preconditioners

2014

RAL-P-2014-016 (PDF(link opens in a new window))
T. Rees and J.A. Scott
The null-space method and its relationship with matrix factorizations for sparse saddle point systems
RAL-P-2014-014 (PDF(link opens in a new window))
C. Cartis, N.I.M. Gould and Ph.L. Toint
Worst-case evaluation complexity of regularization methods for smooth unconstrained optimization using Hölder continuous gradients
RAL-P-2014-013 (PDF(link opens in a new window))
C. Cartis, N.I.M. Gould and Ph.L. Toint
Corrigendum: On the complexity of finding first-order critical pointsb in constrained nonlinear optimization
RAL-P-2014-012 (PDF(link opens in a new window))
N.I.M. Gould, Y. Loh and D.P. Robinson
A filter SQP method : local convergence and numerical results
RAL-P-2014-011 (PDF(link opens in a new window))
F.E. Curtis, N.I.M. Gould, H. Jiang and D.P. Robinson
"Adapting augmented Lagrangian methods: algorithms and practical numerical experience"
RAL-TR-2014-011 (PDF(link opens in a new window))
J.A. Scott
Experiments using incomplete Cholesky factorization preconditioners for saddle-point systems arising in interior-point methods"
RAL-TR-2014-006 (PDF(link opens in a new window))
N.I.M. Gould, C. Ortner and D. Packwood
"An efficient dimer method with preconditioning and linesearch"
RAL-P-2014-007 (PDF(link opens in a new window))
M. Arioli and I.S. Duff
"Preconditioning of linear least-squares problems by identifying basic variables"
RAL-P-2014-006 (PDF(link opens in a new window))
J.D. Hogg, E. Ovtchinnikov and J.A. Scott
"A sparse symmetric indefinite direct solver for GPU architectures"
RAL-P-2014-005 (PDF(link opens in a new window))
L.A. Drummond, I.S. Duff, R. Guivarch, D. Ruiz, and M. Zenadi
"Partitioning strategies for the Block Cimmino algorithm"
RAL-P-2014-004 (PDF(link opens in a new window))
O. Kaya, E. Kayaaslan, B. Uçar, and I.S. Duff
"Fill-in reduction in sparse matrix factorizations using hypergraphs"
RAL-P-2014-003 (PDF(link opens in a new window))
J.A. Scott and M. Tůma
"On signed incomplete Cholesky factorization preconditioners for saddle-point systems"
RAL-P-2014-002 (PDF(link opens in a new window))
J.D. Hogg and J.A. Scott
"On the efficient scaling of sparse symmetric matrices using an auction algorithm"
RAL-P-2014-001 (PDF(link opens in a new window))
F. E. Curtis, N.I.M. Gould, D.P. Robinson and Ph.L. Toint
"An interior-point trust-funnel algorithm for nonlinear optimization"
RAL-TR-2014-001 (PDF (link opens in a new window))
F. E. Curtis, N.I.M. Gould, D.P. Robinson and Ph.L. Toint
"An interior-point trust-funnel algorithm for nonlinear optimization using a squared-violation feasibility measure"

2013

RAL-P-2013-010 (PDF (link opens in a new window))
T. Drummond, I.S. Duff, R. Guivarch, D. Ruiz, and M. Zenadi
"Partitioning strategies for the block Cimmino algorithm"
RAL-P-2013-009 (PDF (link opens in a new window))
C. Cartis, J. M. Fowkes and N.I.M. Gould
"Branching and bounding improvements for global optimization algorithms with Lipschitz continuity properties''
RAL-P-2013-008 (PDF (link opens in a new window))
N.I.M. Gould, Y. Loh and D. D. Robinson
"A filter method with unified step computation for nonlinear optimization''
RAL-P-2013-007 (PDF (link opens in a new window))
J.D. Hogg and J.A. Scott
"Compressed threshold pivoting for sparse symmetric indefinite systems"
RAL-TR-2013-006 (PDF (link opens in a new window))
M. Arioli
"Tensor product of random orthogonal matrices"
RAL-TR-2013-005 (PDF (link opens in a new window))
N.I.M. Gould, D. Orban and Ph.L. Toint
"CUTEst : a constrained testing environment with safe threads''
RAL-TR-2013-004 (PDF (link opens in a new window))
C. Cartis, N.I.M. Gould and Ph.L. Toint
"An example of slow convergence for Newton's method on a function with globally Lipschitz continuous Hessian''
RAL-TR-2013-003 (PDF (link opens in a new window))
M. Arioli and D. Orban
"Iterative methods for symmetric quasi-definite linear systems. Part 1 : theory"
RAL-P-2013-006 (PDF (link opens in a new window))
N.I.M. Gould, D. Orban and T. Rees
"Projected Krylov methods for saddle-point systems''
RAL-P-2013-005 (PDF) (PDF - link opens in a new window)
J.A. Scott and M. Tuma
"On positive semidefinite modification schemes for incomplete Cholesky factorization"
RAL-P-2013-004 (PDF (PDF - link opens in a new window))
J.A. Scott and M. Tuma
"HSL_M128 : an efficient and robust limited-memory incomplete Cholesky factorization code"
RAL-P-2013-003 (PDF (link opens in a new window))
I.S. Duff and K. Kaya
"Preconditioners based on strong subgraphs"
RAL-P-2013-002 (PDF (link opens in a new window))
C. Cartis, N.I.M. Gould and Ph.L. Toint
"On the evaluation complexity of constrained nonlinear least-squares and general constrained nonlinear optimnization using second-order methods"
RAL-P-2013-001 (PDF (link opens in a new window))
I.S. Duff, R. Guivarch, D. Ruiz and M Zenadi
"The augmented block Cimmino distributed method"

2012

RAL-P-2012-009 (PDF (link opens in a new window))
J.D. Hogg and J.A. Scott
"On the effects of scaling on the performance of Ipopt
RAL-P-2012-008 (PDF (link opens in a new window))
P.R. Amestoy, I.S Duff, J-Y L-Excellent and F-H Rouet
"Parallel computation of entries of A inverse"
RAL-TR-2012-020 (PDF (link opens in a new window))
C. Grief, T. Rees and D.B. Szyld.
"Additive Schwarz with variable weights"
RAL-P-2012-006 (PDF (link opens in a new window))
M. Arioli, J. Liesen, A. Miedlar, and Z. Strakos.
"Interplay between discretization and algebraic computation in adaptive numerical solution of elliptic PDE problems."
RAL-P-2012-005 (PDF (link opens in a new window))
J.D. Hogg and J.A. Scott
"Achieving bit compatibility in sparse direct solvers"
RAL-P-2012-004 (PDF (link opens in a new window))
C. Grief, T. Rees and D.B. Szyld
"MPGMRES : a generalized minimum residual method with multiple preconditioners"
RAL-TR-2012-015 (PDF (link opens in a new window))
C. Cartis, N.I.M. Gould and Ph.L. Toint
"On the complexity of the steepest-descent with exact linesearches"
RAL-TR-2012-009 (PDF (link opens in a new window))
J.D. Hogg and J.A. Scott
"A study of pivoting strategies for tough sparse indefinite systems"
RAL-P-2012-003 (PDF (link opens in a new window))
J.D. Hogg and J.A. Scott
"Optimal weighted matchings for rank-deficient sparse matrices"
RAL-P-2012-002 (PDF (link opens in a new window))
J.D. Hogg
"A fast triangular solve on GPUs"
RAL-TR-2012-008 (PDF (link opens in a new window))
C. Cartis, N.I.M. Gould and Ph.L. Toint
"How much patience do you have? A worst-case perspective on smooth nonconvex optimization"
RAL-TR-2012-007 (PDF (link opens in a new window))
C. Cartis, N.I.M. Gould and Ph.L. Toint
"On the evaluation complexity of cubic regularization methods for potentially rank-deficient nonlinear least-squares problems and its relevance to constrained nonlinear optimization"
RAL-TR-2012-001 (PDF (link opens in a new window))
J.A. Scott (ed)
"Numerical Analysis Group Progress Report January 2010 - December 2011"
RAL-P-2012-001 (PDF (link opens in a new window))
J.D. Hogg and J.A. Scott
"New parallel sparse direct solvers for engineering applications"

2011

RAL-TR-2011-026 (PDF (link opens in a new window))
M. Arioli, I.S. Duff, J.D. Hogg and H.S. Thorne
"Guidelines for the development of MATLAB interfaces for HSL packages (revised for MATLAB 2011a)"
RAL-TR-2011-024 (PDF (link opens in a new window))
J.D. Hogg and J.A. Scott
"HSL_MA97 : a bit-compatible multifrontal code for sparse symmetric systems"
RAL-TR-2011-023 (PDF (link opens in a new window))
I.S. Duff
"European Exascale Software Initiative: numerical libraries, solvers, and algorithms"
RAL-TR-2011-022 (PDF (link opens in a new window))
P. A. Browne, C. J. Budd, N.I.M. Gould, H. A. Kim and J.A. Scott
"A fast method for binary programming using first order derivatives, with application to topology optimization with buckling constraints"
RAL-TR-2011-020 (PDF (link opens in a new window))
J. M. Fowkes, N.I.M. Gould and C. L. Farmer
"A branch and bound algorithm for the global optimization of Hessian Lipschitz continuous functions"
RAL-TR-2011-019 (PDF (link opens in a new window))
J.A. Scott and Y. Hu
"Level-based heuristics and hill climbing for the antibandwidth maximization problem"
RAL-TR-2011-017 (PDF (PDF - link opens in a new window))
N.I.M. Gould, D. Orban and D.P. Robinson
"Trajectory-following methods for large-scale degenerate quadratic programming"
RAL-TR-2011-016 (PDF (PDF - link opens in a new window))
C. Cartis, N.I.M. Gould and Ph.L. Toint
"A note about the complexity of minimizing Nesterov's smooth Chebyshev-Rosenbrock function"
RAL-TR-2011-015 (PDF (link opens in a new window))
J.D. Hogg, J.K. Reid and J.A. Scott
"Guidelines for the development of HSL software, 2011 version"
RAL-TR-2011-011 (PDF (link opens in a new window))
C. Cartis, N.I.M. Gould and Ph.L. Toint
"Optimal Newton-type methods for nonconvex smooth optimization problems"
RAL-TR-2011-010 (PDF (link opens in a new window))
M. Arioli and J.A. Scott
"Chebyshev acceleration of iterative refinement"
RAL-TR-2011-009 (PDF (link opens in a new window))
N.I.M. Gould
"How good are extrapolated bi-projection methods for linear feasibility problems?"
RAL-TR-2011-008 (PDF (link opens in a new window))
C. Cartis, N.I.M. Gould and Ph.L. Toint
"On the complexity of finding first-order critical points in constrained nonlinear optimization"
RAL-TR-2011-007 (PDF (link opens in a new window))
N.I.M. Gould, M. Porcelli and Ph.L. Toint
"Updating the regularization parameter in the adaptive cubic regularization algorithm"
RAL-TR-2011-006 (PDF (link opens in a new window))
N.I.M. Gould, D.P. Robinson and Ph.L. Toint
"Corrigendum: nonlinear programming without a penalty function or a filter"
RAL-TR-2011-005 (PDF (link opens in a new window))
C. Cartis, N.I.M. Gould and Ph.L. Toint
"On the evaluation complexity of composite function minimization with applications to nonconvex nonlinear programming"
RAL-TR-2011-002 (PDF (link opens in a new window))
C. Cartis, N.I.M. Gould and Ph.L. Toint
"Complexity bounds for second-order optimality in unconstrained optimization"
RAL-P-2011-001 (PDF (link opens in a new window))
I.S. Duff and K. Kaya
"Preconditioners based on strong components"

2010

RAL-TR-2010-031 (PDF (link opens in a new window))
J.D. Hogg and J.A. Scott
"A modern analyse phase for sparse tree-based direct methods"
RAL-TR-2010-030 (PDF (link opens in a new window))
C. Cartis, N.I.M. Gould and Ph.L. Toint
"Evaluation complexity of adaptive cubic regularization methods for convex unconstrianed optimization"
RAL-TR-2010-029 (PDF (link opens in a new window))
C. Cartis, N.I.M. Gould and Ph.L. Toint
"On the oracle complexity of first-order and derivative-free algorithms for smooth nonconvex minimization"
RAL-TR-2010-027 (PDF (link opens in a new window))
P. R. Amestoy, I.S. Duff, Y. Robert, F.-H. Rouet, and B. Ucar
"On computing inverse entries of a sparse matrix in an out-of-core environment"
RAL-TR-2010-026 (PDF (link opens in a new window))
C. L. Farmer, J. M. Fowkes and N.I.M. Gould
"Optimal multilateral well placement"
RAL-TR-2010-022 (PDF (link opens in a new window))
F. W. Wubs and J. Thies
A robust two-level incomplete factorization for (Navier-)Stokes saddle point matrices"
RAL-TR-2010-019 (PDF (link opens in a new window))
E.E. Ovtchinnkov and J.K. Reid
"A preconditioned block conjugate gradient algorithm for computing extreme eigenpairs of symmetric and Hermitian problems"
RAL-TR-2010-016 (PDF (link opens in a new window))
H.S. Thorne
Distributed control and constraint preconditioners"
RAL-TR-2010-013 (PDF (link opens in a new window))
M. Arioli, I.S. Duff, N.I.M. Gould, J.D. Hogg, and H.S. Thorne
Guidelines for development of Matlab interfaces for HSL packages"
RAL-TR-2010-011 (PDF (link opens in a new window))
J.D. Hogg and J.A. Scott
An indefinite sparse direct solver for large problems on multicore machines"
RAL-TR-2010-008 (PDF (PDF - link opens in a new window))
M. Arioli
Generalized Golub-Kahan bidiagonalization and stopping criteria"
RAL-TR-2010-007 (PDF (link opens in a new window))
J.D. Hogg and J.A. Scott
A note on the solve phase of a multicore solver"
RAL-TR-2010-004 (PDF (link opens in a new window))
J.A. Scott and M. Tuma
The importance of structure in algebraic preconditioners"
RAL-TR-2010-001 (PDF (link opens in a new window))
J.A. Scott
Numerical Analysis Group Progress Report: January 2008 - December 2009"
RAL-P-2010-001 (PDF (link opens in a new window))
I.S. Duff, K. Kaya and B. Ucar
Design, implementation, and analysis of maximum transversal algorithms"

2009

RAL-TR-2009-027 (PDF (PDF - link opens in a new window))
J.D. Hogg, J.K. Reid and J.A. Scott
Design of a multicore sparse Cholesky factorization using DAGs"
RAL-TR-2009-024 (PDF (PDF - link opens in a new window))
N.I.M. Gould and D.P. Robinson
A second-derivative trust-region SQP method with a 'trust-region-free' predictor step"
RAL-TR-2009-023 (PDF (PDF - link opens in a new window))
C. Cartis, N.I.M. Gould and Ph.L. Toint
"On the complexity of steepest descent, Newton's method and regularized Newton methods for nonconvex unconstrained optimization"
RAL-TR-2009-021 (PDF (PDF - link opens in a new window))
M. Arioli, E. H. Georgoulis and D. Login
Convergence of inexact adaptive ﬁnite element solvers for elliptic problems"
RAL-TR-2009-020 (PDF (PDF - link opens in a new window))
M. Arioli
An analysis of GMRES worst case convergence"
RAL-TR-2009-018 (PDF (PDF - link opens in a new window))
H.S. Thorne
Properties of linear systems in PDE-constrained optimization. Part II: Neumann boundary control"
RAL-TR-2009-017 (PDF (PDF - link opens in a new window))
H.S. Thorne
Properties of linear systems in PDE-constrained optimization. Part I: Distributed control"
RAL-TR-2009-016 (PDF (PDF - link opens in a new window))
I.S. Duff and B. Ucar
Combinatorial problems in solving linear systems"
RAL-TR-2009-015 (PDF (PDF - link opens in a new window))
J.K. Reid and J.A. Scott
Partial factorization of a dense symmetric indefinite matrix"
RAL-TR-2009-014 (PDF (PDF - link opens in a new window))
M. Arioli and D. Ruiz
Flexible deflation in Krylov methods with Chebyshev-based polynomial filters"
RAL-TR-2009-013 (PDF (PDF - link opens in a new window))
I.S. Duff and D. Mijuca
On accurate and time efficient solution of primal-mixed finite element equations in multiscale solid mechanics"
RAL-TR-2009-007 (PDF (PDF - link opens in a new window))
J.A. Scott
A note on a simple constrained ordering for saddle-point systems"
RAL-TR-2009-006 (PDF (PDF - link opens in a new window))
C. Cartis, N.I.M. Gould and Ph.L. Toint
"An adaptive cubic regularization algorithm for nonconvex optimization with convex constraints and its function-evaluation complexity"
RAL-TR-2009-004 (revised as RAL-TR-2009-027) (PDF (PDF - link opens in a new window))
J.D. Hogg, J.K. Reid and J.A. Scott
A DAG-based sparse Cholesky solver for multicore architectures"
RAL-TR-2009-003 (PDF (PDF - link opens in a new window))
H.S. Dollar, N.I.M. Gould and D.P. Robinson
On solving trust-region and other regularised subproblems in optimization"
RAL-TR-2009-002 (PDF (PDF - link opens in a new window))
N.I.M. Gould andD.P. Robinson
A second derivative SQP method: local convergence"
RAL-TR-2009-001 (PDF (PDF - link opens in a new window))
N.I.M. Gould andD.P. Robinson
A second derivative SQP method: global convergence"

2008

RAL-TR-2008-031 (PDF (PDF - link opens in a new window))
M. Arioli, D. Kourounis, and D. Loghin
Discrete fractional Sobolev norms for domain decomposition preconditioning"
RAL-TR-2008-029 (revised) (PDF (PDF - link opens in a new window))
J. Hogg
A DAG-based parallel Cholesky factorization for multicore systems"
RAL-TR-2008-028 (PDF (PDF - link opens in a new window))
N.I.M. Gould and V. Simoncini
Spectral analysis of saddle point matrices with indefinite leading blocks"
RAL-TR-2008-027 (PDF (PDF - link opens in a new window)) Supersedes RAL-TR-2006-031
J.K. Reid and J.A. Scott,
Guidelines for the development of HSL software"
RAL-TR-2008-026 (PDF (PDF - link opens in a new window))
S. Bellavia, C. Cartis, N.I.M. Gould, B. Morini and Ph.L. Toint
Convergence of a regularized Euclidean residual algorithm for nonlinear least-squares"
RAL-TR-2008-024 (PDF (PDF - link opens in a new window))
J.K. Reid and J.A. Scott
An efficient out-of-core sparse symmetric indefinite direct solver"
RAL-TR-2008-023 (PDF (PDF - link opens in a new window))
J.D. Hogg and J.A. Scott
A fast and robust mixed precision solver for the solution of sparse symmetric linear systems"
RAL-TR-2008-019 (PDF (PDF - link opens in a new window))
N.I.M. Gould and D.P. Robinson
A second derivative SQP method with imposed descent"
RAL-TR-2008-018 (PDF (PDF - link opens in a new window))
T. Rees, H.S. Dollar and A.J. Wathen
Optimal solvers for PDE-Constrained Optimization"
RAL-TR-2008-017 (PDF (PDF - link opens in a new window))
H.S. Dollar, N.I.M. Gould, M. Stoll and A.J. Wathen
A Bramble-Pasciak-like method with applications in optimization"
RAL-TR-2008-016 (PDF (PDF - link opens in a new window))
J.A. Scott
Scaling and pivoting in an out-of-core sparse direct solver"
RAL-TR-2008-015 (PDF (PDF - link opens in a new window))
J.V. Ashby and J.K. Reid
Migrating a scientific application from MPI to coarrays"
RAL-TR-2008-014 (Revised) (PDF (PDF - link opens in a new window))
I.S. Duff and B. Ucar
On the block triangular form of symmetric matrices"
RAL-TR-2008-013 (PDF (PDF - link opens in a new window))
P.R. Amestoy, I.S. Duff, D. Ruiz, and B. Ucar
"A parallel matrix scaling algorithm"
RAL-TR-2008-012 (PDF (PDF - link opens in a new window))
M. Arioli and D. Loghin
Discrete interpolation norms with applications"
RAL-TR-2008-010 (PDF (PDF - link opens in a new window))
Z.-Z. Bai, I.S. Duff and J.-F. Yin
Numerical study on incomplete orthogonal factorization preconditioners"
RAL-TR-2008-009 (PDF (PDF - link opens in a new window))
I.S. Duff and D. Mijuca
"On the efficient solution of mixed finite element equations in geometrically multiscale thermal stress analysis"
RAL-TR-2008-008 (PDF (PDF - link opens in a new window))
M. Arioli and S. Gratton
Least-squares problems, normal equations, and stopping criteria for the conjugate gradient method"
RAL-TR-2008-007 (PDF (PDF - link opens in a new window))
J.D. Hogg and J.A. Scott
The Effects of Scalings on the Performance of a Sparse Symmetric Indefinite Solver"
RAL-TR-2008-006 (PDF (PDF - link opens in a new window))
M. Arioli and I.S. Duff
Using FGMRES to obtain backward stability in mixed precision"
RAL-TR-2008-005 (PDF (PDF - link opens in a new window))
C. Cartis, N.I.M. Gould and Ph.L. Toint
Trust-region and other regularisations of linear least-squares problems"
RAL-TR-2008-004 (PDF (PDF - link opens in a new window))
M. Arioli
Roundoff error analysis of orthogonal factorizations of upper Hessenberg rectangular matrices"
RAL-TR-2008-003 (PDF (PDF - link opens in a new window))
M. Arioli and D. Loghin
Matrix square-root preconditioners for the Steklov-Poincare operator"
RAL-TR-2008-001 (PDF (PDF - link opens in a new window))
J.A. Scott (Editor)
Numerical Analysis Group Progress Report: January 2006 - December 2007"

2007

RAL-TR-2007-022 (PDF (PDF - link opens in a new window))
H. S. Dollar and J.A. Scott
A note on fast approximate minimum degreeorderings for symmetric matrices with some dense rows"
RAL-TR-2007-021 (PDF (PDF - link opens in a new window))
J. Boyle, M. D. Mihajlovic and J.A. Scott
HSL_MI20: an efficient AMG preconditioner"
RAL-TR-2007-020 (PDF (PDF - link opens in a new window))
P.R. Amestoy, H. S. Dollar, J.K. Reid and J.A. Scott
An approximate minimum degree algorithm for matrices with dense rows"
RAL-TR-2007-016 (PDF (PDF - link opens in a new window))
N.I.M. Gould and Ph.L. Toint
Nonlinear programming without a penalty function or a filter"
RAL-TR-2007-014 (PDF (PDF - link opens in a new window))
J.K. Reid and J.A. Scott
An efficient out-of-core multifrontal solver for large-scale unsymmetric element problems"
RAL-TR-2007-007 (PDF (PDF - link opens in a new window))
C. Cartis, N.I.M. Gould and Ph.L. Toint
Adaptive cubic overestimation methods for unconstrained optimization"
RAL-TR-2007-006 (PDF (PDF - link opens in a new window))
P. Amestoy, I.S. Duff, A. Guermouche, and T. Slavova,
Analysis of the out-of-core solution phase of a parallel multifrontal approach"
RAL-TR-2007-002 (PDF (PDF - link opens in a new window))
I.S. Duff, S. Gratton, X, Pinel, and X. Vasseur,
"Multigrid based preconditioners for the numerical solution of two-dimensional heterogeneous problems in geophysics"
RAL-TR-2007-001 (PDF (PDF - link opens in a new window))
John Reid and Robert W. Numrich,
"Co-arrays in the next Fortran Standard"

2006

RAL-TR-2006-031 (PDF (PDF - link opens in a new window)) Superseded by RAL-TR-2008-027
J.K. Reid and J.A. Scott,
Guidelines for the development of HSL software"
RAL-TR-2006-027 (revised) (PDF (PDF - link opens in a new window))
I.S. Duff,
The design and use of a sparse direct solver for skew symmetric matrices"
RAL-TR-2006-026 (revised) (PDF (PDF - link opens in a new window))
J.K. Reid and J.A. Scott,
HSL_OF01, a virtual memory system in Fortran"
RAL-TR-2006-016 (PDF (PDF - link opens in a new window))
C. Cartis and N.I.M. Gould,
Finding a point in the relative interior of a polyhedron"
RAL-TR-2006-015 (PDF (PDF - link opens in a new window))
N.I.M. Gould,
How good are projection methods for convex feasibility problems?"
RAL-TR-2006-014 (PDF (PDF - link opens in a new window))
I.S. Duff,
Sparse system solution and the HSL Library"
RAL-TR-2006-013 (revised) (PDF (PDF - link opens in a new window))
J.K. Reid and J.A. Scott,
"An out-of-core sparse Cholesky solver"
RAL-TR-2006-010 (PDF (PDF - link opens in a new window))
M. Arioli and D. Loghin,
Stopping criteria for mixed finite element problems"
RAL-TR-2006-007 (PDF (PDF - link opens in a new window))
M. Arioli, I.S. Duff, S. Gratton, and S. Pralet,
"A note on GMRES preconditioned by a perturbed LDL^T decomposition with static pivoting"
RAL-TR-2006-006 (PDF (PDF - link opens in a new window))
I.S. Duff (Editor),
"Numerical Analysis Group Progress Report. January 2004 - December 2005."
RAL-TR-2006-001 (PDF (PDF - link opens in a new window))
I.S. Duff and J.A. Scott,
"Towards an automatic ordering for a symmetric sparse direct solver"

2005

RAL-TR-2005-026 (PDF (PDF - link opens in a new window))
H.S. Dollar, N.I.M. Gould, W.H.A. Schilders and A.J. Wathen,
"Using constraint preconditioners with regularized saddle-point problems"
RAL-TR-2005-014 (PDF (PDF - link opens in a new window))
J.A. Scott and Y. Hu,
Experiences of sparse direct symmetric solvers"
RAL-TR-2005-011 (PDF (PDF - link opens in a new window))
H.S. Dollar, N.I.M. Gould, W.H.A. Schilders and A.J. Wathen,
"On iterative methods and implicit-factorization preconditioners for regularized saddle-point systems"
RAL-TR-2005-007 (PDF (PDF - link opens in a new window))
I.S. Duff and S. Pralet,
"Towards a stable static pivoting strategy for the sequential and parallel solution of sparse symmetric indefinite systems"
RAL-TR-2005-005 (PDF (PDF - link opens in a new window))
N.I.M. Gould, Y. Hu and J.A. Scott,
"A numerical evaluation of sparse direct symmetric solvers for the solution of large sparse, symmetric linear systems of equations"
RAL-TR-2005-004 (PDF (PDF - link opens in a new window))
M. Arioli and G. Manzini,
"MI31: a conjugate gradient algorithm implementation with energy-norm stopping criteria"
RAL-TR-2005-001 (PDF (PDF - link opens in a new window))
J.K. Reid and J.A. Scott,
Reducing the total bandwidth of a sparse unsymmetric matrix"

2004

RAL-TR-2004-040 (PDF (PDF - link opens in a new window))
I.S. Duff, S. Riyavong and M. B. Van Gijzen,
Parallel preconditioners based on partitioning sparse matrices"
RAL-TR-2004-036 (PDF (PDF - link opens in a new window))
H.S. Dollar, N.I.M. Gould and A.J. Wathen,
On implicit-factorization constraint preconditioners"
RAL-TR-2004-033 (Revised) (PDF (PDF - link opens in a new window))
I.S. Duff,
"Combining direct and iterative methods for the solution of large systems in different application areas"
RAL-TR-2004-032 (PDF (PDF - link opens in a new window))
N.I.M. Gould, D. Orban and Ph.L. Toint,
Numerical methods for large-scale nonlinear optimization"
RAL-TR-2004-031 (PDF (PDF - link opens in a new window))
R. H. Byrd, N.I.M. Gould, J. Nocedal and R. A. Waltz
"On the convergence of successive linear-quadratic programming algorithms"
RAL-TR-2004-030 (PDF (PDF - link opens in a new window))
N.I.M. Gould, D. Orban, A. Sartenaer and Ph.L. Toint,
Sensitivity of trust-region algorithms to their parameters"
RAL-TR-2004-029 (PDF (PDF - link opens in a new window))
M. Arioli, M. Baboulin, and S. Gratton,
Partial condition number for linear least-squares problems"
RAL-TR-2004-026 (PDF (PDF - link opens in a new window))
J.A. Scott
"MA42_ELEMENT - a state-of-the-art frontal solver for finite-element applications"
RAL-TR-2004-020 (PDF (PDF - link opens in a new window))
I.S. Duff and S. Pralet,
"Strategies for scaling and pivoting for sparse symmetric indefinite problems"
RAL-TR-2004-018 (PDF (PDF - link opens in a new window))
J.A. Scott
Multilevel hybrid spectral element ordering algorithms"
RAL-TR-2004-017 (PDF (PDF - link opens in a new window))
B. S. Andersen, J.A. Gunnels, F. G. Gustavson, J.K. Reid, and J. Wasniewski,
"A fully portable high performance minimal storage hybrid format Cholesky algorithm"
RAL-TR-2004-016 (PDF (PDF - link opens in a new window))
I.S. Duff (Editor),
"Numerical Analysis Group Progress Report. January 2002 - December 2003."
RAL-TR-2004-009 (PDF (PDF - link opens in a new window))
N.I.M. Gould, C. Sainvitu and Ph.L. Toint,
A filter-trust-region method for unconstrained optimization"
RAL-TR-2004-006 (PDF (PDF - link opens in a new window))
I.S. Duff and J.A. Scott
"Stabilized bordered block diagonal forms for parallel sparse solvers"

2003

RAL-TR-2003-036 (PDF (PDF - link opens in a new window))
Y. Hu and J.A. Scott
HSL_MC73: A fast multilevel Fiedler and profile reduction code"
RAL-TR-2003-024 (PDF (PDF - link opens in a new window))
B. Carpentieri, I.S. Duff, L. Giraud, and G. Sylvand,
"Combining fast multipole techniques and an approximate inverse preconditioner for large electromagnetism calculations"
RAL-TR-2003-023 (PDF (PDF - link opens in a new window))
I.S. Duff, L. Giraud, J. Langou, and E. Martin,
"Using spectral low rank preconditioners for large electromagnetic calculations"
RAL-TR-2003-022 (PDF (PDF - link opens in a new window))
N.I.M. Gould, D. Orban and Ph.L. Toint,
"An interior-point l₁-penalty method for nonlinear optimization"
RAL-TR-2003-020 (PDF (PDF - link opens in a new window))
Y. Hu and J.A. Scott
"Ordering techniques for singly bordered block diagonal forms for unsymmetric parallel sparse direct solvers"
RAL-TR-2003-019 (PDF (PDF - link opens in a new window))
N.I.M. Gould and J.A. Scott
"A numerical evaluation of HSL packages for the direct solution of large sparse, symmetric linear systems of equations"
RAL-TR-2003-017 (PDF (PDF - link opens in a new window))
N.I.M. Gould and Ph.L. Toint
"FILTRANE, a fortran 95 filter-trust-region package for solving nonlinear feasibility problems"
FUNDP 03/04 (PDF (PDF - link opens in a new window))
N.I.M. Gould and Ph.L. Toint
"How mature is nonlinear optimization?"
RAL-TR-2003-013 (PDF (PDF - link opens in a new window))
R. H. Byrd, N.I.M. Gould, J. Nocedal and R. A. Waltz
On the convergence of successive linear programming algorithms"
RAL-TR-2003-009 (PDF (PDF - link opens in a new window))
M. Arioli, D. Loghin, and A.J. Wathen
Stopping criteria for iterations in finite-element methods"
RAL-TR-2003-004 (PDF (PDF - link opens in a new window))
N.I.M. Gould, S. Leyffer and Ph.L. Toint
"A multidimensional Filter algorithm for nonlinear equations and nonlinear least squares"
RAL-TR-2003-003 (PDF (PDF - link opens in a new window))
N.I.M. Gould and Ph.L. Toint
"Global convergence of a non-monotone trust-region SQP-Filter algorithm for nonlinear programming"

2002

RAL-TR-2002-034 (PDF (PDF - link opens in a new window))
M. Arioli,
"A stopping criterion for the Conjugate Gradient algorithm in a finite element method framework"
RAL-TR-2002-033 (PDF (PDF - link opens in a new window))
I.S. Duff and J.A. Scott,
"A parallel direct solver for large sparse highly unsymmetric linear systems"
RAL-TR-2002-032 (PDF (PDF - link opens in a new window))
R. H. Byrd, N.I.M. Gould, J. Nocedal and R. A. Waltz,
"An active set algorithm for nonlinear programming using linear programming and equality constrained subproblems"
RAL-TR-2002-031 (PDF (PDF - link opens in a new window))
N.I.M. Gould and S. Leyffer,
An introduction to algorithms for nonlinear optimization"
RAL-TR-2002-030 (PDF (PDF - link opens in a new window))
J.K. Reid,
"The new features of Fortran 2000"
RAL-TR-2002-029 (PDF (PDF - link opens in a new window))
S.A. Forth, M. Tadjouddine, J.D. Pryce and J.K. Reid,
"Jacobian code generated by source transformation and vertex elimination is as efficient as hand coding"
RAL-TR-2002-028 (PDF (PDF - link opens in a new window))
P. R. Amestoy, I.S. Duff, and C. Voemel,
"Task scheduling in an asynchronous distributed memory multifrontal solver"
RAL-TR-2002-026 (PDF (PDF - link opens in a new window))
M. Arioli and G. Manzini,
"Null space algorithm and spanning trees in solving Darcy's equation"
RAL-TR-2002-024 (PDF (PDF - link opens in a new window))
I.S. Duff,
"MA57 - A new code for the solution of sparse symmetric definite and indefinite systems"
RAL-TR-2002-021 (PDF (PDF - link opens in a new window))
M. Arioli and D. Ruiz,
"A Chebyshev-based two-stage iterative method as an alternative to the direct solution of linear systems"
RAL-TR-2002-020 (PDF (PDF - link opens in a new window))
B. Carpentieri, I.S. Duff, and L. Giraud,
A class of spectral two-level preconditioners"
RAL-TR-2002-019 (PDF (PDF - link opens in a new window))
A. T. Papadopoulos, I.S. Duff, and A. T. Wathen,
"A class of incomplete orthogonal factorization methods. II: implementation and results"
RAL-TR-2002-018 (PDF (PDF - link opens in a new window))
I.S. Duff and C. Voemel,
"Algorithm xxx: a reference model implementation of the Sparse BLAS in Fortran 95"
RAL-TR-2002-016 (PDF (PDF - link opens in a new window))
B. Carpentieri, I.S. Duff, L. Giraud, and M. Magolu monga Made,
"Sparse symmetric preconditioners for dense linear systems in electromagnetism"
RAL-TR-2002-014 (PDF (PDF - link opens in a new window))
N.I.M. Gould, D. Orban and Ph.L. Toint,
"GALAHAD, a library of thread-safe Fortran 90 packages for large-scale nonlinear optimization"
RAL-TR-2002-012 (PDF (PDF - link opens in a new window))
J.A. Scott,
Parallel frontal solvers for large sparse linear systems"
RAL-TR-2002-010 (PDF (PDF - link opens in a new window))
I.S. Duff (Editor),
"Numerical Analysis Group Progress Report. January 2000 - December 2001."
RAL-TR-2002-009 (PDF (PDF - link opens in a new window))
N.I.M. Gould, D. Orban and Ph.L. Toint,
"CUTEr (and SifDec), a Constrained and Unconstrained Testing Environment, revisited"
RAL-TR-2002-001 (PDF (PDF - link opens in a new window))
N.I.M. Gould and Ph.L. Toint,
"Preprocessing for quadratic programming"

2001

RAL-TR-2001-039 (PDF (PDF - link opens in a new window))
J.K. Reid and J.A. Scott
"Implementing Hager's exchange methods for matrix profile reduction"
RAL-TR-2001-037 (PDF (PDF - link opens in a new window))
M. Arioli and G. Manzini
"A network programming approach in solving Darcy's equations by mixed finite-element methods"
RAL-TR-2001-034 (PDF (PDF - link opens in a new window))
D. Ruiz,
"A scaling algorithm to equilibrate both row and column norms in matrices"
RAL-TR-2001-033 (PDF (PDF - link opens in a new window))
N.I.M. Gould and Ph.L. Toint,
"Global convergence of a hybrid trust-region SQP-Filter algorithm for general nonlinear programming"
RAL-TR-2001-032 (PDF (PDF - link opens in a new window))
I.S. Duff, M. A. Heroux, and R. Pozo,
"The Sparse BLAS"
RAL-TR-2001-026 (PDF (PDF - link opens in a new window))
N.I.M. Gould and Ph.L. Toint,
"An iterative working-set method for large-scale non-convex quadratic programming"
RAL-TR-2001-023 (PDF (PDF - link opens in a new window))
M. Arioli, J. Maryska, M. Rozloznik, and M. Tuma,
"Dual variable methods for mixed-hybrid finite element approximation of the potential fluid flow problem in porous media"
RAL-TR-2001-017 (PDF (PDF - link opens in a new window))
N.I.M. Gould and Ph.L. Toint,
"Numerical methods for large-scale non-convex quadratic programming"
RAL-TR-2001-011 (PDF (PDF - link opens in a new window))
J.A. Scott,
"The design of a portable parallel frontal solver for chemical process engineering problems"
RAL-TR-2001-006 (PDF (PDF - link opens in a new window))
M. Arioli and G. Manzini,
"A null space algorithm for mixed finite element approximation of Darcy's equation"
RAL-TR-2001-005 (PDF (PDF - link opens in a new window))
I.S. Duff and C. Voemel,
Incremental norm estimation for dense and sparse matrices"
RAL-TR-2001-004 (PDF (PDF - link opens in a new window))
P. R. Amestoy, I.S. Duff, J.-Y. L'Excellent, and X. S. Li,
"Performance and tuning of two distributed memory sparse solvers"
RAL-TR-2001-003 (PDF (PDF - link opens in a new window))
P. R. Amestoy, I.S. Duff, J.-Y. L'Excellent, and X. S. Li,
"Analysis and comparison of two general sparse solvers for distributed memory computers"

2000

RAL-TR-2000-040 (PDF (PDF - link opens in a new window))
N.I.M. Gould, D. Orban, A. Sartenaer and Ph.L. Toint,
"Componentwise fast convergence in the solution of full-rank systems of nonlinear equations"
RAL-TR-2000-031 (PDF (PDF - link opens in a new window))
Y. F. Hu and J.A. Scott,
Multilevel algorithms for wavefront reduction"
RAL-TR-2000-030 (PDF (PDF - link opens in a new window))
J.A. Scott,
"Two-stage ordering for unsymmetric parallel row-by-row frontal solvers"
RAL-TR-2000-014 (PDF (PDF - link opens in a new window))
N.I.M. Gould, D. Orban, A. Sartenaer and Ph.L. Toint,
"Superlinear convergence of primal-dual interior point algorithms for nonlinear programming"
RAL-TR-2000-011 (PDF (PDF - link opens in a new window))
K. Meerbergen and J.A. Scott,
"The design of a block rational Lanczos code with partial reorthogonalization and implicit restarting"
RAL-TR-2000-010 (PDF (PDF - link opens in a new window))
K. Meerbergen,
The Lanczos method with semi-inner product"
RAL-TR-2000-009 (PDF (PDF - link opens in a new window))
B. Carpentieri, I.S. Duff, and L. Giraud,
"Some sparse pattern selection strategies for robust Frobenius norm minimization preconditioners in electromagnetism"
RAL-TR-2000-001 (PDF (PDF - link opens in a new window))
I.S. Duff (Editor),
"Numerical Analysis Group Progress Report. January 1998 - December 1999."

1999

RAL-TR-1999-075 (PDF (PDF - link opens in a new window))
J.A. Scott,
"The design of a parallel frontal solver"
RAL-TR-1999-072 (PDF (PDF - link opens in a new window))
I.S. Duff,
"The impact of high performance computing in the solution of linear systems: trends and problems"
RAL-TR-1999-059 (PDF (PDF - link opens in a new window))
P. R. Amestoy, I.S. Duff, J.-Y. L'Excellent, and J.Koster,
"A fully asynchronous multifrontal solver using distributed dynamic scheduling"
RAL-TR-1999-055 (PDF (PDF - link opens in a new window))
N.I.M. Gould and Ph.L. Toint,
SQP methods for large-scale nonlinear programming"
RAL-TR-1999-054 (PDF (PDF - link opens in a new window))
A. R. Conn, N.I.M. Gould, D. Orban and Ph.L. Toint,
"A primal-dual trust-region algorithm for minimizing a non-convex function subject to general inequality and linear equality constraints"
RAL-TR-1999-045 (PDF (PDF - link opens in a new window))
Z.-Z. Bai, I.S. Duff, and A.J. Wathen,
"A class of incomplete orthogonal factorization methods I: methods and theories"
RAL-TR-1999-041 (PDF (PDF - link opens in a new window))
R. Fletcher, N.I.M. Gould, S. Leyffer and Ph.L. Toint,
"Global convergence of trust-region SQP-filter algorithms for general nonlinear programming"
RAL-TR-1999-039 (PDF (PDF - link opens in a new window))
F. Magoules, K. Meerbergen and J.-P. Coyette,
"Application of a domain decomposition method with Lagrange multipliers to acoustic problems arising from the automotive industry"
RAL-TR-1999-030 (PDF (PDF - link opens in a new window))
I.S. Duff and Jacko Koster,
"On algorithms for permuting large entries to the diagonal of a sparse matrix"
RAL-TR-1999-037 (PDF (PDF - link opens in a new window))
J.K. Reid and J.A. Scott,
Reversing the row order for the row-by-row frontal method"
RAL-TR-1999-035 (PDF (PDF - link opens in a new window))
J.A. Scott,
"Row ordering for frontal solvers in chemical process engineering"
RAL-TR-1999-027 (PDF (PDF - link opens in a new window))
I.S. Duff and H. A. van der Vorst,
"Developments and trends in the parallel solution of linear systems"
RAL-TR-1999-025 (PDF (PDF - link opens in a new window))
K. Meerbergen,
"The rational Lanczos method for the Hermitian eigenvalue problem"
RAL-TR-1999-016 (PDF (PDF - link opens in a new window))
C. Keller, N.I.M. Gould and A.J. Wathen,
Constraint preconditioning for indefinite linear systems"
RAL-TR-1999-011 (PDF (PDF - link opens in a new window))
K. Meerbergen,
Locking and restarting quadratic eigenvalue solvers"

1998

RAL-TR-1998-076 (PDF (PDF - link opens in a new window))
I.S. Duff,
"Matrix methods"
RAL-TR-1998-069 (PDF (PDF - link opens in a new window))
N.I.M. Gould, M. E. Hribar and J. Nocedal,
"On the solution of equality constrained quadratic programming problems arising in optimization"
RAL-TR-1998-064 (PDF (PDF - link opens in a new window))
N.I.M. Gould,
"Iterative methods for ill-conditioned linear systems from optimization"
RAL-TR-1998-060 (PDF (PDF - link opens in a new window))
R. W. Numrich and J.K. Reid,
Co-Array Fortran for parallel programming"
RAL-TR-1998-057 (PDF (PDF - link opens in a new window))
J.D. Pryce and J.K. Reid,
AD01, a Fortran 90 code for automatic differentitation"
RAL-TR-1998-056 (PDF (PDF - link opens in a new window))
J.A. Scott,
A new row ordering strategy for frontal solvers"
RAL-TR-1998-054 (PDF (PDF - link opens in a new window))
I.S. Duff,
"Direct Methods"
RAL-TR-1998-052 (PDF (PDF - link opens in a new window))
I.S. Duff and H. A. van der Vorst,
Preconditioning and Parallel Preconditioning"
RAL-TR-1998-051 (PDF (PDF - link opens in a new window))
P. Amestoy, I. Duff, and J.-Y. L'Excellent,
"Multifrontal Parallel Distributed Symmetric and Unsymmetric Solvers"
RAL-TR-98-039 (PDF (PDF - link opens in a new window))
P. Amestoy, I. Duff, J.-Y. L'Excellent, and P. Plechac,
"PARASOL An Integrated Programming Environment for Parallel Sparse Matrix Solvers"
RAL-TR-98-031 (PDF (PDF - link opens in a new window))
J.A. Scott,
On ordering elements for a frontal solver"
RAL-TR-98-028 (PDF (PDF - link opens in a new window))
I.S. Duff (Editor),
"Numerical Analysis Group Progress Report. January 1996 - December 1997"
RAL-TR-98-027 (PDF (PDF - link opens in a new window))
J.K. Reid,
Implicit scaling of linear least squares problems"
RAL-TR-98-016 (PDF (PDF - link opens in a new window))
J.K. Reid and J.A. Scott,
"Ordering symmetric sparse matrices for small profile and wavefront"
RAL-TR-98-005 (PDF (PDF - link opens in a new window))
M.J. Daydé, J. Décamps and N.I.M. Gould,
"Subspace-by-Subspace preconditioners for structured linear systems"
RAL-TR-98-003 (PDF (PDF - link opens in a new window))
N.I.M. Gould, S. Lucidi, M. Roma and Ph.L. Toint,
"A linesearch algorithm with memory for unconstrained optimization"

1997

RAL-TR-97-071 (PDF (PDF - link opens in a new window))
N.I.M. Gould and J. Nocedal,
"The modified absolute-value factorization norm for trust-region minimization"
ENSEEIHT RT/APO/97/3 (PDF (PDF - link opens in a new window))
M.J. Daydé, J. Décamps and N.I.M. Gould,
"Solution of Unassembled Linear Systems Using Block Stretching: Preliminary Experiments"
RAL-TR-97-064 (PDF (PDF - link opens in a new window))
N.I.M. Gould, S. Lucidi, M. Roma and Ph.L. Toint,
"Exploiting Negative Curvature Directions in Linesearch Methods for Unconstrained Optimization"
RAL-TR-97-059 (PDF (PDF - link opens in a new window))
I.S. Duff and Jacko Koster,
"The design and use of algorithms for permuting large entries to the diagonal"
RAL-TR-97-058 (PDF (PDF - link opens in a new window))
"R. B. Lehoucq and J.A. Scott,
"Implicitly restarted Arnoldi methods and eigenvalues of the discretized Navier Stokes equations"
RAL-TR-97-055 (PDF (PDF - link opens in a new window))
N.I.M. Gould and Ph.L. Toint,
"A note on the second-order convergence of optimization algorithms using barrier functions"
FUNDP 97/14 (PDF (PDF - link opens in a new window))
I. Bongartz, A. R. Conn, N.I.M. Gould, M. A. Saunders and Ph.L. Toint,
"A numerical comparison between the LANCELOT and MINOS packages for large-scale constrained optimization: the complete results"
RAL-TR-97-054 (PDF (PDF - link opens in a new window))
I. Bongartz, A. R. Conn, N.I.M. Gould, M. A. Saunders and Ph.L. Toint,
"A numerical comparison between the LANCELOT and MINOS packages for large-scale constrained optimization"
RAL-TR-97-046 (PDF (PDF - link opens in a new window))
T. A. Davis and I.S. Duff,
"A combined unifrontal/multifrontal method for unsymmetric sparse matrices"
RAL-TR-97-041 (PDF (PDF - link opens in a new window))
J.A. Scott,
"Exploiting zeros in frontal solvers"
RAL-TR-97-031 (PDF (PDF - link opens in a new window))
I.S. Duff and R. G. Grimes and J. G. Lewis,
The Rutherford-Boeing Sparse Matrix Collection"
RAL-TR-97-028 (PDF (PDF - link opens in a new window))
N.I.M. Gould, S. Lucidi, M. Roma and Ph.L. Toint,
Solving the trust-region subproblem using the Lanczos method"
RAL-TR-97-012 (PDF (PDF - link opens in a new window))
I.S. Duff and J.A. Scott,
"MA62 - A frontal code for sparse positive-definite symmetric systems from finite-element applications"
RAL-TR-97-001 (PDF (PDF - link opens in a new window))
K. A. Cliffe, I.S. Duff and J.A. Scott,
"Performance issues for frontal schemes on a cache-based high performance computer"

1996

CERFACS TR/PA/96/47 (PDF (PDF - link opens in a new window))
M.J.Daydé and I.S. Duff,
"Use of Computational Kernels in full and Sparse Linear Solvers, Efficient Code Design on High-Performance RISC Processors"
RAL-TR-96-102 (Revised) (PDF (PDF - link opens in a new window))
I.S. Duff and J.A. Scott,
"A comparison of frontal software with other Harwell Subroutine Library sparse direct solvers"
RAL-TR-96-102 (PDF (PDF - link opens in a new window))
I.S. Duff and J.A. Scott,
"A comparison of frontal software with other sparse direct solvers"
RAL-TR-96-096 (PDF (PDF - link opens in a new window))
A. R. Conn, N.I.M. Gould and Ph.L. Toint,
"A primal-dual algorithm for minimizing a non-convex function subject to bound and linear equality constraints"
RAL-TR-96-047 (PDF (PDF - link opens in a new window))
I.S. Duff,
"Sparse numerical linear algebra: direct methods and preconditioning"
RAL-TR-96-042 (PDF (PDF - link opens in a new window))
A. R. Conn, N.I.M. Gould and Ph.L. Toint,
Methods for Nonlinear Constraints in Optimization Calculations"
TOMS-96-22, pp.30-45. (PDF (PDF - link opens in a new window))
I.S. Duff and J.A. Scott,
"The design of a new frontal code for solving sparse unsymmetric systems"
RAL-TR-96-023 (PDF (PDF - link opens in a new window))
R. B. Lehoucq and J.A. Scott,
"An evaluation of Arnoldi based software for sparse nonsymmetric eigenproblems"
RAL-TR-96-022 (PDF (PDF - link opens in a new window))
R. B. Lehoucq and J.A. Scott,
"An evaluation of subspace iteration software for sparse nonsymmetric eigenproblems"
RAL-TR-96-015 (PDF (PDF - link opens in a new window))
I.S. Duff (Editor),
"Numerical Analysis Group - Progress report. January 1994 - December 1995"
RAL-TR-96-014 (PDF (PDF - link opens in a new window))
M.J.Daydé and I.S. Duff,
A Blocked Implementation of Level 3 BLAS for RISC Processors"
RAL-TR-96-013 (PDF (PDF - link opens in a new window))
J. Cardenal, I.S. Duff, and J. M. Jimenez,
A projection method for the solution of rectangular systems"
RAL-TR-96-010 (PDF (PDF - link opens in a new window))
A. C. Damhaug and J.K. Reid,
"MA46, a FORTRAN code for direct solution of sparse unsymmetric linear systems of equations from finite-element applications"

1995

RAL-TR-95-049 (PDF (PDF - link opens in a new window))
I.S. Duff, M. Marrone, G. Radicati, and C. Vittoli,
"Level 3 Basic Linear Algebra Subprograms for sparse matrices: a user level interface"
RAL-TR-95-040 (PDF (PDF - link opens in a new window))
I.S. Duff and J.K. Reid,
"Exploiting zeros on the diagonal in the direct solution of indefinite sparse symmetric linear systems"
RAL-TR-95-039 (PDF (PDF - link opens in a new window))
I.S. Duff and J.K. Reid,
"The design of MA48, a code for the direct solution of sparse unsymmetric linear systems of equations"
RAL-TR-95-037 (PDF (PDF - link opens in a new window))
N.I.M. Gould,
"Constructing appropriate models for large-scale, linearly-constrained, nonconvex, nonlinear optimization algorithms"
RAL-95-027 (PDF (PDF - link opens in a new window))
J.A. Scott,
Element resequencing for use with a multiple front algorithm"
RAL-TR-95-026 (PDF (PDF - link opens in a new window))
N.I.M. Gould and J.A. Scott,
"On approximate-inverse preconditioners"
RAL-93-097 (revised) (PDF (PDF - link opens in a new window))
J.A. Scott,
"An Arnoldi code for computing selected eigenvalues of sparse real unsymmetric matrices (revised)"
RAL-95-009 (PDF (PDF - link opens in a new window))
A. R. Conn, N.I.M. Gould, A. Sartenaer and Ph.L. Toint,
"Convergence Properties of an Augmented Lagrangian Algorithm for Optimization with a Combination of General Equality and Linear Constraints"
RAL-95-001 (PDF (PDF - link opens in a new window))
I.S. Duff and J.K. Reid,
"MA47, a Fortran code for direct solution of sparse symmetric linear systems of equations"

1994

RAL-94-069 (PDF (PDF - link opens in a new window))
A. R. Conn, N.I.M. Gould, A. Sartenaer and Ph.L. Toint,
"On Iterated-Subspace Minimization Methods for Nonlinear Optimization"
RAL-94-062 (PDF (PDF - link opens in a new window))
I.S. Duff (Editor),
"Numerical Analysis Group - Progress report. January 1991 - December 1993"
RAL-94-040 (PDF (PDF - link opens in a new window))
I.S. Duff and J.A. Scott,
The use of multiple fronts in Gaussian elimination"
RAL-94-019 (PDF (PDF - link opens in a new window))
M.J.Daydé and I.S. Duff,
"Porting industrial codes and developing sparse linear solvers on parallel computers"
ENSEEIHT RT/APO/94/4 (PDF (PDF - link opens in a new window)) or RAL-95-010
M.J.Daydé, J.-Y. L'Excellent and N.I.M. Gould,
"On the Use of Element-by-Element Preconditioners to Solve Large Scale Partially Separable Optimization Problems"
CERFACS TR/PA/94/10 (PDF (PDF - link opens in a new window))
I.S. Duff and M.J.Daydé,
"The CERFACS experience"
CERFACS TR/PA/94/03 (PDF (PDF - link opens in a new window))
A. R. Conn, N.I.M. Gould and Ph.L. Toint,
"Large-scale nonlinear constrained optimization: a current survey"

1993

RAL-93-097 (PDF (PDF - link opens in a new window))
J.A. Scott,
"An Arnoldi code for computing selected eigenvalues of sparse real unsymmetric matrices"
RAL-93-084 (PDF (PDF - link opens in a new window))
I.S. Duff,
"The solution of augmented systems"
RAL-93-072 (PDF (PDF - link opens in a new window))
I.S. Duff and J.K. Reid,
"MA48, a Fortran code for direct solution of sparse unsymmetric linear systems of equations"
RAL-93-066 (PDF (PDF - link opens in a new window)) or CERFACS TR/PA/93/34
M. Arioli, T. F. Chan, I.S. Duff, N.I.M. Gould and J.K. Reid,
"Computing a search direction for large-scale linearly-constrained nonlinear optimization calculations"
RAL-93-064 (PDF (PDF - link opens in a new window))
I.S. Duff and J.A. Scott,
"MA42 - A new frontal code for solving sparse unsymmetric systems"
RAL-93-036 (PDF (PDF - link opens in a new window))
T. A. Davis and I.S. Duff,
"An unsymmetric-pattern multifrontal method for sparse LU factorization"
CERFACS TR/PA/93/27 (PDF (PDF - link opens in a new window))
A. R. Conn, N.I.M. Gould, A. Sartenaer and Ph.L. Toint,
"Local Convergence Properties of two Augmented Lagrangian Algorithms for Optimization with a Combination of General Equality and Linear Constraints"
CERFACS TR/PA/93/26 (PDF (PDF - link opens in a new window))
A. R. Conn, N.I.M. Gould, A. Sartenaer and Ph.L. Toint,
"Global Convergence of two Augmented Lagrangian Algorithms for Optimization with a Combination of General Equality and Linear Constraints"
CERFACS TR/PA/93/17 (PDF (PDF - link opens in a new window))
A. R. Conn, N.I.M. Gould and Ph.L. Toint,
"A note on using alternative second-order models for the subproblems arising in barrier function methods for minimization"
CERFACS TR/PA/93/16 (PDF (PDF - link opens in a new window))
A. R. Conn, N.I.M. Gould and Ph.L. Toint,
"Improving the decomposition of partially separable functions in the context of large-scale optimization: A first approach"
CERFACS TR/PA/93/10 (PDF (PDF - link opens in a new window)) or the published version in ACM TOMS (PDF (PDF - link opens in a new window))
I. Bongartz, A. R. Conn, N.I.M. Gould and Ph.L. Toint,
CUTE: constrained and unconstrained testing environment"

1992

RAL-92-086 (PDF (PDF - link opens in a new window))
I.S. Duff, R. G. Grimes and J. G. Lewis,
"Users' Guide for the Harwell-Boeing Sparse Matrix Collection (Release I)"
RAL-92-069 (PDF (PDF - link opens in a new window))
A. R. Conn, N.I.M. Gould and Ph.L. Toint,
"Convergence properties of minimization algorithms for convex constraints using a structured trust region"
RAL-92-068 (PDF (PDF - link opens in a new window))
A. R. Conn, N.I.M. Gould and Ph.L. Toint,
"On the number of inner iterations per outer iteration of a globally convergent algorithm for optimization with general nonlinear inequality constraints and simple bounds"
RAL-92-067 (PDF (PDF - link opens in a new window))
A. R. Conn, N.I.M. Gould and Ph.L. Toint,
"A globally convergent Lagrangian barrier algorithm for optimization with general inequality constraints and simple bounds"
RAL-92-017 (PDF (PDF - link opens in a new window))
J.K. Reid,
"The advantages of Fortran 90"
FUNDP 92/17 (PDF (PDF - link opens in a new window))
A. R. Conn, N.I.M. Gould and Ph.L. Toint,
A note on exploiting structure when using slack variables"
FUNDP 92/16 (PDF (PDF - link opens in a new window))
A. R. Conn, N.I.M. Gould and Ph.L. Toint,
"Numerical experiments with the LANCELOT package (Release A) for large-scale nonlinear optimization"
FUNDP 92/15 (PDF (PDF - link opens in a new window))
A. R. Conn, N.I.M. Gould and Ph.L. Toint,
"Intensive numerical tests with LANCELOT (Release A): the complete results"
CERFACS TR/PA/92/89 (PDF (PDF - link opens in a new window))
P. R. Amestoy, M.J.Daydé, I.S. Duff and P. Morere,
Linear algebra calculations on a virtual shared memory computer"
CERFACS TR/PA/92/74 (PDF (PDF - link opens in a new window))
M.J.Daydé, I.S. Duff, and A. Petitet,
"A parallel block implementation of Level 3 BLAS for MIMD vector processors"

1991

RAL-91-056 (PDF (PDF - link opens in a new window))
I.S. Duff and J.A. Scott,
"Computing selected eigenvalues of sparse unsymmetric matrices using subspace iteration"

1970 - 1990

AERE-R10533 (1982) (PDF (PDF - link opens in a new window))
I.S. Duff and J.K. Reid
MA27 -- A Set of Fortran Subroutines for Solving Sparse Symmetric Sets of Linear Equations"
AERE-R8629 (1976) (PDF (PDF - link opens in a new window))
J.K. Reid
Fortran subroutines for handling sparse linear programming bases"
AERE-TP515 (1973) (PDF (PDF - link opens in a new window))
M. D. Hebden
An algorithm for minimization using exact second derivatives"
AERE-R7125 (1972) (PDF (PDF - link opens in a new window))
R. Fletcher
Fortran subroutines for minimization by quasi-Newton methods"
AERE-R6799 (1971) (PDF (PDF - link opens in a new window))
R. Fletcher
A modified Marquardt subroutine for non-linear least squares"
AERE-R6469 (1970) (PDF (PDF - link opens in a new window))
M.J.D. Powell
"A Fortran subroutine for unconstrained minimization, requiring first derivatives of the objective function"
AERE-R5947 (1968) (PDF (PDF - link opens in a new window))
M.J.D. Powell
A Fortran subroutine for solving systems of non-linear algebraic equations"
AERE-TP322 (1968) (PDF (PDF - link opens in a new window))
M.J.D. Powell and J.K. Reid
"On applying Householder transformations to linear least squares problems"

The group has also issued the following Numerical Analysis Group Internal Reports:

2023-2 (PDF (PDF - link opens in a new window))
N.I.M. Gould
Linear least-squares over the unit simplex"
2023-1 (PDF (PDF - link opens in a new window))
N.I.M. Gould
A projection method for bound-constrained linear least-squares"
2013-1 (PDF (PDF - link opens in a new window))
N.I.M. Gould
"Computing useful sparse Hessian approximations satisfying componentwise secant equations I: using a known sparsity pattern"
2011-1 (PDF (PDF - 433kB - link opens in a new window))
J.D. Hogg.
"C interfaces to HSL routines"
2009-2 (PDF (PDF - link opens in a new window))
N. I. M. Gould, M. Kocvara, D. P. Robinson and Ph. L. Toint
Enriched recursive multi-level optimization"
2009-1 (PDF (PDF - link opens in a new window))
H.S. Dollar
On Taylor series approximations for trust-region and regularized subproblems in optimization"
2007-1 (PDF (PDF - link opens in a new window))
N.I.M. Gould
"Equivalent saddle-point problems"
2006-1 (PDF (PDF - link opens in a new window))
N.I.M. Gould
A brief note on the Symmetric Rank-1 secant formula"
2005-1 revised: (PDF (PDF - link opens in a new window)), original: (PDF (PDF - link opens in a new window))
N.I.M. Gould, Y. Hu and J.A. Scott.
"Complete results from a numerical evaluation of sparse direct solvers for the solution of large, sparse, symmetric linear systems of equations"
2004-2 (PDF (PDF - link opens in a new window))
N.I.M. Gould
Parametric quadratic programming, revisited"
2004-1 (PDF (PDF - link opens in a new window))
J.A. Scott, Y. Hu and N.I.M. Gould
"An evaluation of sparse direct symmetric solvers: an introduction and preliminary findings"
2003-2 (PDF (PDF - link opens in a new window))
N.I.M. Gould and J.A. Scott
"Complete results from a numerical evaluation of HSL packages for the direct-solution of large sparse, symmetric linear systems of equations"
2003-1 (PDF (PDF - link opens in a new window))
N.I.M. Gould
"Some reflections on the current state of active-set and interior-point methods for constrained optimization"
2002-1 (PDF (PDF - link opens in a new window))
N.I.M. Gould, D. Orban and Ph.L. Toint
Results from a numerical evaluation of LANCELOT B"
2000-1 (PDF (PDF - link opens in a new window))
N.I.M. Gould and Ph.L. Toint
"A Quadratic Programming Bibliography"