一类高秩大规模 T-Stein 方程的分解 Smith 方法

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

数学季刊 ›› 2024, Vol. 39 ›› Issue (3): 235-249.doi: 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

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

收稿日期:2023-07-14 出版日期:2024-09-30 发布日期:2024-09-30
通讯作者: YU Bo (1979-), male, native of Zhuzhou, Hunan, associate professor of Hunan University of Technology, engages in scientific engineering computation; E-mail:boyu hut@126.com
作者简介: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.
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).

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

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

Received:2023-07-14 Online:2024-09-30 Published:2024-09-30
Contact: YU Bo (1979-), male, native of Zhuzhou, Hunan, associate professor of Hunan University of Technology, engages in scientific engineering computation; E-mail:boyu hut@126.com
About author: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.
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).

摘要/Abstract

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

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

中图分类号:

O241

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.

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.

[1]	唐忠华, 房少梅. 带分数阶Robin边界条件的时间-空间分数阶扩散方程的有限差分方法[J]. 数学季刊, 2024, 39(1): 18-30.
[2]	曾敏, 袁永新. 一个2×2块矩阵的Moore-Penrose逆的显式公式[J]. 数学季刊, 2023, 38(4): 401-409.
[3]	黄卓红. 奇异鞍点问题中广义位移分裂迭代方法的半收敛性分析[J]. 数学季刊, 2023, 38(2): 145-156.
[4]	刘丽娜, 袁钰莹, 袁永新. 利用特征结构配置方法修正质量和刚度矩阵[J]. 数学季刊, 2021, 36(4): 419-429.
[5]	张士君, 王世恒, 王珂. 耦合Lyapunov 矩阵方程的AOR迭代法[J]. 数学季刊, 2021, 36(2): 141-148.
[6]	许铭修, 黎景辉. 随机变量的共轭梯度方法[J]. 数学季刊, 2021, 36(2): 111-121.
[7]	林海欣 , 房少梅, . 带有分数阶Robin边界条件的Riesz空间分数阶对流-扩散方程的有限差分方法[J]. 数学季刊, 2020, 35(3): 278-289.
[8]	曹南斌, 张玉平. 矩阵方程组AX=C;XB=D{P;k+1}-反射解的研究[J]. 数学季刊, 2018, 33(1): 32-42.
[9]	陈爱敏, 刘发旺. 有限体积方法非结构网格方法解分数阶Allen-Cahn程[J]. 数学季刊, 2017, 32(4): 345-354.
[10]	王俊杰, 李胜平. GSDBM方程的多辛几何和多辛Preissman格式研究 [J]. 数学季刊, 2017, 32(2): 172-180.
[11]	王志军, 郝晓斌, 石东洋. 定常Navier-Stokes方程的一个二阶非协调三角型混合元格式[J]. 数学季刊, 2017, 32(1): 88-98.
[12]	马燕. 时间分数阶扩散方程的一种隐式差分方法分析[J]. 数学季刊, 2016, 31(1): 69-81.
[13]	张红梅. 热方程紧差分格式重叠型区域分解算法[J]. 数学季刊, 2015, 30(4): 495-502.
[14]	孙佳, 王世恒, 王珂. 鞍点问题PHSS方法预条件的新取法[J]. 数学季刊, 2015, 30(4): 555-561.
[15]	郑华盛. 关于数值微分公式的两个注记[J]. 数学季刊, 2012, 27(4): 480-484.

一类高秩大规模 T-Stein 方程的分解 Smith 方法

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

PDF (PC)

可视化

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 15

GSDBM方程的多辛几何和多辛Preissman格式研究

编辑推荐

Metrics

本文评价