9 papers
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…
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…
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…
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…
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…