Hussam Al Daas

Senior Computational Mathematician

Numerical Linear Algebra

Hussam is a researcher in the Computational Mathematics Theme (CMT) at STFC Rutherford Appleton Laboratory and a Visiting Research Fellow in the Numerical Analysis Group at the University of Oxford. Hussam received his masters in fundamental and applied mathematics from Paris-sud University in 2014. He received a PhD in Numerical Analysis at Inria-Paris and Sorbonne University (Paris-VI) in 2018. Afterwards, he spent 18 months as a postdoctoral fellow in the Computational Methods in Control and System Theory Group in the Max Planck Institute in Magdeburg, Germany. Starting from August 2020, he joined CMT.

His research interests lie in the fields of numerical linear and multilinear algebra and high-performance computing. In particular, he is interested in solving large-scale sparse linear systems using preconditioned (accelerated) iterative methods focusing on acceleration techniques that are algebraic (no dependency on the underlying problem), robust with respect to problems parameters, and scalable.

  • High performance computing
  • Domain decomposition
  • Low-rank tensor methods
  • Krylov subspace methods

Preprints:

  • 3- Matrix perturbation analysis of methods for extracting singular values from approximate singular subspaces. 2024. Preprint
    L. Lazzarino, H. Al Daas, Y. Nakatsukasa

  • 2- Communication Lower Bounds and Optimal Algorithms for Symmetric Matrix Computations. 2024. Preprint
    H. Al Daas, G. Ballard, L. Grigori, S. Kumar, K. Rouse, M. Verite

  • 1- A Robust Two-Level Schwarz Preconditioner For Sparse Matrices. 2024. Preprint
    H. Al Daas, P. Jolivet, F. Nataf, P.-H. Tournier

Publications:

  • 14- Communication Lower Bounds and Optimal Algorithms for Multiple Tensor-Times-Matrix Computation.
    SIAM J. Matrix Anal. Appl., 45(1), 450--477. 2024. Paper, preprint
    H. Al Daas, G. Ballard, L. Grigori, S. Kumar, K. Rouse

  • 13- Parallel Memory-Independent Communication Bounds for SYRK.
    SPAA 2023 Proceedings. Paper, Preprint.
    H. Al Daas, G. Ballard, L. Grigori, S. Kumar, K. Rouse

  • 12- Efficient Algebraic Two-Level Schwarz Preconditioner For Sparse Matrices.
    SIAM J. Sci. Comput., 45(3), A1199--A1213. 2023. Paper, preprint
    H. Al Daas, P. Jolivet, T. Rees

  • 11- Randomized algorithms for rounding in the Tensor-Train format.
    SIAM J. Sci. Comput. 45(1), A74--A95. 2023. Paper.
    H. Al Daas, G. Ballard, P. Cazeaux, E. Hallman, A. Miedlar, M. Pasha, T. W. Reid, A. K. Saibaba
    Matlab code for reproducing the results available here.

  • 10- A Robust Algebraic Multilevel Domain Decomposition Preconditioner For Sparse Symmetric Positive Definite Matrices.
    SIAM J. Sci. Comput., 44(4), A2582--A2598. 2022. Paper preprint
    H. Al Daas, P. Jolivet

  • 9- Brief Announcement: Tight Memory-Independent Parallel Matrix Multiplication Communication Lower Bounds.
    SPAA 2022 Proceedings. Paper.
    H. Al Daas, G. Ballard, L. Grigori, S. Kumar, K. Rouse

  • 8- Parallel Tensor Train Rounding using Gram SVD.
    IPDPS 2022 Proceedings. Paper .
    H. Al Daas, G. Ballard, L. Maning

  • 7- A Robust Algebraic Domain Decomposition Preconditioner for Sparse Normal Equations.
    SIAM J. Sci. Comput., 44(3), A1047--A1068. 2022. journal, preprint.
    H. Al Daas, P. Jolivet, J. Scott
    Code for reproducing the results available here, PETSc interface through the HPDDM package, PCHPDDM.

  • 6- Parallel Algorithms for Tensor Train Arithmetic.
    SIAM J. Sci. Comput., 44(1), C25--C53. 2022. journal, preprint
    H. Al Daas, G. Ballard, P. Benner
    MPI Algorithms for Tensor-Train Arithmetic (MPI_ATTAC) is a library implementing algorithms in the paper. It is available here.

  • 5- Two-level Nyström--Schur preconditioner for sparse symmetric positive definite matries
    SIAM J. Sci. Comput., 43(6), A3837--A3861. 2021. journal, preprint
    H. Al Daas, T. Rees, J. Scott
    Code for reproducing numerical experiments available here.

  • 4- A Multilevel Schwarz Preconditioner Based on a Hierarchy of Robust Coarse Spaces.
    SIAM J. Sci. Comput., 43(3), A1907--A1928. 2021. journal, preprint
    H. Al Daas, L. Grigori, P. Jolivet, P. H. Tournier
    Code for reproducing the results available here, PETSc interface through the HPDDM package, PCHPDDM.

  • 3- Recycling Krylov Subspaces and Truncating Deflation Subspaces for Solving Sequence of Linear Systems.
    ACM Transactions on Mathematical Software Volume 47 Issue 2 June 2021 Article No.: 13 pp 1--30. journal, preprint.
    H. Al Daas, L. Grigori, P. Henon, P. Ricoux

  • 2- A Class of Efficient Locally Constructed Preconditioners Based on Coarse Spaces.
    SIAM J. Matrix Anal. Appl., 40(1), 66--91. 2019. journal, preprint.
    H. Al Daas, L. Grigori

  • 1- Enlarged GMRES for solving linear systems with one or multiple right-hand sides.
    IMA Journal of Numerical Analysis, Vol. 39, 2019, pp. 1924--1956. 2019. journal.
    H. Al Daas, L. Grigori, P. Henon, P. Ricoux

Technical Reports:

  • 3- Tight Memory-Independent Parallel Matrix Multiplication Communication Lower Bounds. 2022. preprint
    H. Al Daas, G. Ballard, L. Grigori, S. Kumar, K. Rouse

  • 2- An extended Krylov-like method for the solution of multi-linear systems. 2021. preprint
    H. Al Daas, D. Lombardi

  • 1- Low-Rank and Total Variation Regularization and Its Application to Image Recovery. 2020. preprint.
    P. Goyal, H. Al Daas, P. Benner

Domain decomposition preconditioners:

  • A Robust Two-Level Schwarz Preconditioner For Sparse Matrices.
    PETSc interface through the HPDDM package, PCHPDDM.

  • Efficient Algebraic Two-Level Schwarz Preconditioner For Sparse Matrices.
    PETSc interface through the HPDDM package, PCHPDDM.

  • A Robust Algebraic Multilevel Domain Decomposition Preconditioner For Sparse Symmetric Positive Definite Matrices.
    PETSc interface through the HPDDM package, PCHPDDM.

  • A Robust Algebraic Domain Decomposition Preconditioner for Sparse Normal Equations.
    Code for reproducing the results available here.
    Soon: PETSc interface through the HPDDM package, PCHPDDM.

  • Two-level Nyström--Schur preconditioner for sparse symmetric positive definite matries
    Code for reproducing numerical experiments available here.

  • A Multilevel Schwarz Preconditioner Based on a Hierarchy of Robust Coarse Spaces.
    Code for reproducing the results available here.
    PETSc interface through the HPDDM package, PCHPDDM.

Low rank tensor computations:

  • HSL_MP82 .
    Parallel orthonormalization procedures (QR and SVD) for tall-skinny matrices: TSQR, CholQR, CholQR2, CholQR3 and Gram-based SVD here. This is part of the Harwell Subroutine Library (HSL).

  • Randomized algorithms for rounding in the Tensor-Train format.
    Matlab code for reproducing the results available here.

  • MPI_ATTAC Parallel Algorithms for Tensor Train Arithmetic.
    MPI Algorithms for Tensor-Train Arithmetic (MPI_ATTAC) is a library implementing algorithms in the paper. It is available here.

  • PI on Reliable and efficient tensor sketching algorithms using structured random matrices. Collaboration with Yuji Nakatsukasa (Oxford). £74K Jan-2024 to Dec-2024 ESPRC funding
  • Co-I on Numerical Analysis Procurement, NEPTUNE, ExCALIBUR. STFC team. Sept-2022 to Mar-2024
  • Co-I on Mathematical Support for Software Implementation, NEPTUNE, ExCALIBUR. STFC team. Sept-2021 to Sept-2022
  • Co-I on A divide and conquer attack on challenging least squares problems. (with J. Scott PI) £80K Nov-2021 to Oct-2022 EPSRC funding

  • Technical Paper Committee Member of the Algorithms Area in Super Computing 2024.

  • 2022-2024 SIAM UKIE Secretary and Treasurer .

  • Technical Paper Committee Member of Area 1: Applications, Algorithms, and Libraries in IEEE Cluster 2022.

  • Co-organizer of the Online series Communication in Numerical Linear Algebra.

  • Programm Committee Member of TOPIC 10: PARALLEL NUMERICAL METHODS AND APPLICATIONS in EURO-PAR 2020.