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BIMSA Computational Math Seminar
New error bounds and applications of low synchronization orthogonalization algorithms
New error bounds and applications of low synchronization orthogonalization algorithms
Organizers
Tahereh Eftekhari
,
Pipi Hu
,
Xin Liang
,
Zhiting Ma
,
Hamid Mofidi
, Chunmei Su
,
Axel G.R. Turnquist
,
Li Wang
,
Fansheng Xiong
,
Shuo Yang
,
Wuyue Yang
Speaker
Qinmeng Zou
Time
Wednesday, April 1, 2026 2:00 PM - 3:00 PM
Venue
A3-4-312
Online
Zoom 518 868 7656
(BIMSA)
Abstract
Modified Gram-Schmidt (MGS) is a traditional QR factorization process that is widely used in solving linear systems and least squares problems. For example, the generalized minimal residual method (GMRES) usually employs QR factorization to orthogonalize the basis of Krylov subspace. This talk discusses a class of low-synchronization MGS algorithms, denoted as MGS-LTS, which can date back to Bjorck's work in 1967. We give a stability analysis of MGS-LTS, proving that the loss of orthogonality of its basic form as well as the block and normalization lagging variants is proportional to the condition number. We also discuss the probabilistic tools and investigate the causes of instability of the Cholesky-based block variant. Finally, numerical experiments are presented to show the practical behavior of such kind of algorithms. In particular, we report performance tests on sparse linear systems using mixed precision GMRES and sparse approximate inverse preconditioning.