Preconditioned tensor format conjugate gradient squared and biconjugate gradient stabilized methods for solving stein tensor equations

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2023-05-10 DOI:10.1002/nla.2502

Yuhan Chen, Chenliang Li

引用次数: 0

Abstract

This article is concerned with solving the high order Stein tensor equation arising in control theory. The conjugate gradient squared (CGS) method and the biconjugate gradient stabilized (BiCGSTAB) method are attractive methods for solving linear systems. Compared with the large‐scale matrix equation, the equivalent tensor equation needs less storage space and computational costs. Therefore, we present the tensor formats of CGS and BiCGSTAB methods for solving high order Stein tensor equations. Moreover, a nearest Kronecker product preconditioner is given and the preconditioned tensor format methods are studied. Finally, the feasibility and effectiveness of the new methods are verified by some numerical examples.

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预条件张量格式求解stein张量方程的共轭梯度平方和双共轭梯度稳定方法

本文讨论了控制理论中的高阶Stein张量方程的求解问题。共轭梯度平方（CGS）方法和双共轭梯度稳定（BiCGSTAB）方法是求解线性系统的有吸引力的方法。与大型矩阵方程相比，等效张量方程需要更少的存储空间和计算成本。因此，我们提出了求解高阶Stein张量方程的CGS和BiCGSTAB方法的张量格式。此外，给出了最近Kronecker乘积预条件，并研究了预条件张量格式的方法。最后，通过算例验证了新方法的可行性和有效性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.