An Uzawa-DOS method for solving saddle-point problems

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-07-06 DOI:10.1007/s11075-024-01873-1

Ghodrat Ebadi, Khosro Mehrabi, Predrag S. Stanimirović

引用次数: 0

Abstract

Based on the diagonal and off-diagonal splitting (DOS) iteration scheme (Dehghan et al. Filomat 31(5), 1441–1452 2017), we offer an iteration procedure called Uzawa-DOS to solve a class of saddle-point problems (SPPs). Each iteration of this iterative method involves two subsystems with diagonal and lower triangular matrices. Due to the simple structure of involved coefficient matrices, two linear subsystems are solvable exactly, which is a notable precedence of the Uzawa-DOS method and can make it inexpensive to execute. Theoretical analysis verifies convergence of the proposed method under appropriate conditions. The suggested method is validated by numerical experiments.

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解决鞍点问题的乌泽-DOS 方法

基于对角线和非对角线分割（DOS）迭代方案（Dehghan et al. Filomat 31(5), 1441-1452 2017），我们提供了一种名为 Uzawa-DOS 的迭代程序，用于解决一类鞍点问题（SPP）。这种迭代法的每次迭代都涉及两个具有对角矩阵和下三角矩阵的子系统。由于涉及的系数矩阵结构简单，两个线性子系统可以精确求解，这是 Uzawa-DOS 方法的一个显著先例，可以使其执行成本低廉。理论分析验证了所提方法在适当条件下的收敛性。数值实验验证了所建议的方法。

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.