2 citations · 4 across the 20 of their papers we have counts for
14 papers · 1 filter
Two-level convergence of Algebraic Multigrid with Overlapping Smoothers and Spectral Coarse Grids
O. A. Krzysik, B. S. Southworth, H. Al Daas
We recently developed the least-squares algebraic-multigrid domain-decomposition (LS-AMG-DD) solver as an algebraic multilevel method for sparse symmetric positive definite matrice…
Efficient Sketching-Based Summation of Tucker Tensors
Rudi Smith, Mirjeta Pasha, Andrés Galindo-Olarte +5
We present efficient, sketching-based methods for the summation of tensors in Tucker format. Leveraging the algebraic structure of Khatri-Rao and Kronecker products, our approach e…
Algebraic Multigrid with Overlapping Schwarz Smoothers and Local Spectral Coarse Grids for Least Squares Problems
Ben S. Southworth, Hussam Al Daas, Golo A. Wimmer +1
This paper develops a new algebraic multigrid (AMG) method for sparse least-squares systems of the form motivated by challenging applications in scientific computing where…
Adaptive Randomized Tensor Train Rounding using Khatri-Rao Products
Hussam Al Daas, Grey Ballard, Laura Grigori +3
Approximating a tensor in the tensor train (TT) format has many important applications in scientific computing. Rounding a TT tensor involves further compressing a tensor that is a…
Extended-Krylov-subspace methods for trust-region and norm-regularization subproblems
Hussam Al Daas, Nicholas I. M. Gould
We consider an effective new method for solving trust-region and norm-regularization problems that arise as subproblems in many optimization applications. We show that the solution…
Minimal residual rational Krylov subspace method for sequences of shifted linear systems
Hussam Al Daas, Davide Palitta
The solution of sequences of shifted linear systems is a classic problem in numerical linear algebra, and a variety of efficient methods have been proposed over the years. Neverthe…
Matrix perturbation analysis of methods for extracting singular values from approximate singular subspaces
Lorenzo Lazzarino, Hussam Al Daas, Yuji Nakatsukasa
Given (orthonormal) approximations and to the left and right subspaces spanned by the leading singular vectors of a matrix , we discuss methods to approx…
A Robust Two-Level Schwarz Preconditioner For Sparse Matrices
Hussam Al Daas, Pierre Jolivet, Frédéric Nataf +1
This paper introduces a fully algebraic two-level additive Schwarz preconditioner for general sparse large-scale matrices. The preconditioner is analyzed for symmetric positive def…
Efficient Algebraic Two-Level Schwarz Preconditioner For Sparse Matrices
Hussam Al Daas, Pierre Jolivet, Tyrone Rees
Domain decomposition methods are among the most efficient for solving sparse linear systems of equations. Their effectiveness relies on a judiciously chosen coarse space. Originall…
Randomized algorithms for rounding in the Tensor-Train format
Hussam Al Daas, Grey Ballard, Paul Cazeaux +5
The Tensor-Train (TT) format is a highly compact low-rank representation for high-dimensional tensors. TT is particularly useful when representing approximations to the solutions o…
A Robust Algebraic Multilevel Domain Decomposition Preconditioner For Sparse Symmetric Positive Definite Matrices
Hussam Al Daas, Pierre Jolivet
Domain decomposition (DD) methods are widely used as preconditioner techniques. Their effectiveness relies on the choice of a locally constructed coarse space. Thus far, this const…
A Robust Algebraic Domain Decomposition Preconditioner for Sparse Normal Equations
Hussam Al Daas, Pierre Jolivet, Jennifer Scott
Solving the normal equations corresponding to large sparse linear least-squares problems is an important and challenging problem. For very large problems, an iterative solver is ne…
Two-level Nyström--Schur preconditioner for sparse symmetric positive definite matrices
Hussam Al Daas, Tyrone Rees, Jennifer Scott
Randomized methods are becoming increasingly popular in numerical linear algebra. However, few attempts have been made to use them in developing preconditioners. Our interest lies…
Parallel Algorithms for Tensor Train Arithmetic
Hussam Al Daas, Grey Ballard, Peter Benner
We present efficient and scalable parallel algorithms for performing mathematical operations for low-rank tensors represented in the tensor train (TT) format. We consider algorithm…