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math.NA2025
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…
cs.DC2025
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…
math.NA2025
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…