Factorized Smith Method for A Class of High-Ranked Large-Scale T-Stein Equations

LI Xiang, YU Bo, TANG Qiong

doi:10.13371/j.cnki.chin.q.j.m.2024.03.002

Chinese Quarterly Journal of Mathematics >

2024 , Vol. 39 >Issue 3: 235 - 249

DOI: https://doi.org/10.13371/j.cnki.chin.q.j.m.2024.03.002

Factorized Smith Method for A Class of High-Ranked Large-Scale T-Stein Equations

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School of Science, Hunan University of Technology, Zhuzhou 412007, China

LI Xiang (1999-), female, native of Fuyang, Anhui, master student of Hunan University of Technology, engages in numerical algebra; YU Bo (1979-), male, native of Zhuzhou, Hunan, associate professor of Hunan University of Technology, engages in scientific engineering computation; TANG Qiong (1972-), female, native of Liuyang, Hunan, professor of Hunan University of Technology, engages in numerical analysis.

Received date: 2023-07-14

Online published: 2024-09-30

Supported by

Supported partly by NSF of China (Grant No. 11801163); NSF of Hunan Province (Grant Nos. 2021JJ50032, 2023JJ50164 and 2023JJ50165); Degree & Postgraduate Reform Project of Hunan University of Technology and Hunan Province (Grant Nos. JGYB23009 and 2024JGYB210).

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Abstract

We introduce a factorized Smith method (FSM) for solving large-scale highranked J-Stein equations within the banded-plus-low-rank structure framework. To effectively reduce both computational complexity and storage requirements, we develop techniques including deflation and shift, partial truncation and compression, as well as redesign the residual computation and termination condition. Numerical examples demonstrate that the FSM outperforms the Smith method implemented with a hierarchical
HODLR structured toolkit in terms of CPU time.

Key words： Large-scale T-Stein equations; High-ranked; Deflation and shift; Partially truncation and compression; Smith method

Cite this article

LI Xiang, YU Bo, TANG Qiong . Factorized Smith Method for A Class of High-Ranked Large-Scale T-Stein Equations[J]. Chinese Quarterly Journal of Mathematics, 2024 , 39(3) : 235 -249 . DOI: 10.13371/j.cnki.chin.q.j.m.2024.03.002

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