数学季刊 >

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

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

一类高秩大规模 T-Stein 方程的分解 Smith 方法

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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.

收稿日期: 2023-07-14

  网络出版日期: 2024-09-30

基金资助

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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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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摘要

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.

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

本文引用格式

李想, 余波, 汤琼 . 一类高秩大规模 T-Stein 方程的分解 Smith 方法[J]. 数学季刊, 2024 , 39(3) : 235 -249 . DOI: 10.13371/j.cnki.chin.q.j.m.2024.03.002

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

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