An Uzawa-DOS method for solving saddle-point problems

IF 1.7 3区数学 Q2 MATHEMATICS, APPLIED

Numerical Algorithms 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

Numerical Algorithms 数学-应用数学

CiteScore

4.00

自引率

9.50%

发文量

201

审稿时长

9 months

期刊介绍： The journal Numerical Algorithms is devoted to numerical algorithms. It publishes original and review papers on all the aspects of numerical algorithms: new algorithms, theoretical results, implementation, numerical stability, complexity, parallel computing, subroutines, and applications. Papers on computer algebra related to obtaining numerical results will also be considered. It is intended to publish only high quality papers containing material not published elsewhere.