求解Stein张量方程的张量格式BCGSTAB算法

数学物理学报 ›› 2024, Vol. 44 ›› Issue (6): 1652-1664.

求解Stein张量方程的张量格式BCGSTAB算法

马昌凤¹(),谢亚君^1,^*(),卜凡²()

¹福州外语外贸学院大数据学院, 数据科学与智能计算重点实验室福州 350202
²福建师范大学数学与信息学院福州 350117

收稿日期:2023-12-29 修回日期:2024-05-06 出版日期:2024-12-26 发布日期:2024-11-22
通讯作者: ^*谢亚君,Email：xyj@fzfu.edu.cn
作者简介:马昌凤,Email：mcf@fzfu.edu.cn;|卜凡,Email：2669299068@qq.com
基金资助:
国家自然科学基金(12371378);福建省自然科学基金(2024J01980)

The Tensor Scheme BCGSTAB Algorithm for Solving Stein Tensor Equations

Ma Changfeng¹(),Xie Yajun^1,^*(),Bu Fan²()

¹School of Big Data & Key Laboratory of Data science and intelligent computing, Fuzhou University of International Studies and Trade, Fuzhou 350202
²School of Mathematics and Information, Fujian Normal University, Fuzhou 350117

Received:2023-12-29 Revised:2024-05-06 Online:2024-12-26 Published:2024-11-22
Supported by:
NSFC(12371378);Natural Science Foundation of Fujian Province(2024J01980)

摘要/Abstract

摘要：

双共轭梯度稳定化方法(BCGSTAB) 是双共轭梯度方法的快速和光滑收敛的变形. 该文将 BCGSTAB 算法推广到求解 Stein 张量方程, 给出了张量格式的算法以及解的存在性的具体证明过程, 并得到了该算法的收敛性结果. 数值实验证实了该算法用于求解 Stein 张量方程是有效且可行的.

关键词: Stein 张量方程, BCGSTAB 算法, 收敛性分析, 数值实验

Abstract:

The biconjugate gradient stabilized (BCGSTAB) method is a fast and smoothly converging variant of biconjugate gradient (BiCG) method. In this paper, we generalize BCGSTAB method to solve the Stein tensor equation. We raise the algorithm of tensor format and specific proof process of existence of a solution. And we present the convergence theorem of this algorithm. Numerical experiments demonstrate this algorithm is effective and feasible for solving the Stein tensor equation.

Key words: tein tensor equation, BCGSTAB method, Convergence analysis, Numerical experiment

中图分类号:

O241.1

马昌凤, 谢亚君, 卜凡. 求解Stein张量方程的张量格式BCGSTAB算法[J]. 数学物理学报, 2024, 44(6): 1652-1664.

Ma Changfeng, Xie Yajun, Bu Fan. The Tensor Scheme BCGSTAB Algorithm for Solving Stein Tensor Equations[J]. Acta mathematica scientia,Series A, 2024, 44(6): 1652-1664.

图/表 5

参考文献 21

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