5 papers · 1 filter
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…
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…