6 citations · 6 across the 9 of their papers we have counts for
11 papers
Asynchronous Jacobi and randomized Gauss--Seidel methods in shared and distributed memory: A unified convergence-rate analysis
Erin Carson, Yuxin Ma
Asynchronous iterative methods are attractive for large-scale parallel computing because they reduce synchronization and communication overhead. Existing convergence-rate analyses,…
Hybrid hierarchical matrices with adaptive mixed precision storage
Ritesh Khan, Erin Carson
Hierarchical matrices are data-sparse approximations of dense matrices that are widely used for fast matrix computations. Hierarchical matrices are built using a tree data structur…
Mixed precision thin SVD algorithms based on the Gram matrix
Erin Carson, Yuxin Ma, Meiyue Shao
In this work, we present a mixed precision algorithm that leverages the Gram matrix and Jacobi methods to compute the singular value decomposition (SVD) of tall-and-skinny matrices…
Forward and backward error bounds for a mixed precision preconditioned conjugate gradient algorithm
Thomas Bake, Erin Carson, Yuxin Ma
The preconditioned conjugate gradient (PCG) algorithm is one of the most popular algorithms for solving large-scale linear systems , where is a symmetric positive defin…
The Performance of Low-Synchronization Variants of Reorthogonalized Block Classical Gram--Schmidt
Erin Carson, Yuxin Ma
Numerous applications, such as Krylov subspace solvers, make extensive use of the block classical Gram-Schmidt (BCGS) algorithm and its reorthogonalized variants for orthogonalizin…
On the numerical stability of sketched GMRES
Liam Burke, Erin Carson, Yuxin Ma
We perform a backward stability analysis of preconditioned sketched GMRES [Nakatsukasa and Tropp, SIAM J. Matrix Anal. Appl, 2024] for solving linear systems , and show that…
A stable one-synchronization variant of reorthogonalized block classical Gram--Schmidt
Erin Carson, Yuxin Ma
The block classical Gram--Schmidt (BCGS) algorithm and its reorthogonalized variant are widely-used methods for computing the economic QR factorization of block columns due to…
On the backward stability of s-step GMRES
Erin Carson, Yuxin Ma
Communication, i.e., data movement, is a critical bottleneck for the performance of classical Krylov subspace method solvers on modern computer architectures. Variants of these met…
On the loss of orthogonality in low-synchronization variants of reorthogonalized block classical Gram-Schmidt
Erin Carson, Kathryn Lund, Yuxin Ma +1
Interest in communication-avoiding orthogonalization schemes for high-performance computing has been growing recently. This manuscript addresses open questions about the numerical…
Reorthogonalized Pythagorean variants of block classical Gram-Schmidt
Erin Carson, Kathryn Lund, Yuxin Ma +1
Block classical Gram-Schmidt (BCGS) is commonly used for orthogonalizing a set of vectors in distributed computing environments due to its favorable communication properties re…
Mixed Precision FGMRES-Based Iterative Refinement for Weighted Least Squares
Erin Carson, Eda Oktay
With the recent emergence of mixed precision hardware, there has been a renewed interest in its use for solving numerical linear algebra problems fast and accurately. The solution…