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New error bounds and applications of low synchronization orthogonalization algorithms

组织者

Tahereh Eftekhari , 胡丕丕 , 梁鑫 , 马志婷 , 哈米德·莫菲迪 , 苏春梅 , Axel G.R. Turnquist , 王丽 , 熊繁升 , 杨朔 , 杨武岳

演讲者

邹秦萌

时间

2026年04月01日 14:00 至 15:00

地点

A3-4-312

线上

Zoom 518 868 7656 (BIMSA)

摘要

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.