2 citations · 4 across the 20 of their papers we have counts for
21 papers
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…
Communication Lower Bounds and Algorithms for Sketching with Random Dense Matrices
Hussam Al Daas, Grey Ballard, Laura Grigori +4
Sketching is widely used in randomized linear algebra for low-rank matrix approximation, column subset selection, and many other problems, and it has gained significant traction in…
Reducing acquisition time and radiation damage: data-driven subsampling for spectro-microscopy
Maike Meier, Lorenzo Lazzarino, Boris Shustin +2
Spectro-microscopy is an experimental technique which can be used to observe spatial variations in chemical state and changes in chemical state over time or under experimental cond…
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…
Minimizing Communication for Parallel Symmetric Tensor Times Same Vector Computation
Hussam Al Daas, Grey Ballard, Laura Grigori +3
In this article, we focus on the parallel communication cost of multiplying the same vector along two modes of a -dimensional symmetric tensor. This is a key computation in the…
Communication Lower Bounds and Optimal Algorithms for Symmetric Matrix Computations
Hussam Al Daas, Grey Ballard, Laura Grigori +3
In this article, we focus on the communication costs of three symmetric matrix computations: i) multiplying a matrix with its transpose, known as a symmetric rank-k update (SYRK) i…
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…
Communication Lower Bounds and Optimal Algorithms for Multiple Tensor-Times-Matrix Computation
Hussam Al Daas, Grey Ballard, Laura Grigori +2
Multiple Tensor-Times-Matrix (Multi-TTM) is a key computation in algorithms for computing and operating with the Tucker tensor decomposition, which is frequently used in multidimen…
Tight Memory-Independent Parallel Matrix Multiplication Communication Lower Bounds
Hussam Al Daas, Grey Ballard, Laura Grigori +2
Communication lower bounds have long been established for matrix multiplication algorithms. However, most methods of asymptotic analysis have either ignored the constant factors or…
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…
Low-Rank and Total Variation Regularization and Its Application to Image Recovery
Pawan Goyal, Hussam Al Daas, Peter Benner
In this paper, we study the problem of image recovery from given partial (corrupted) observations. Recovering an image using a low-rank model has been an active research area in da…