An accelerated MSOR-Like method for solving specific saddle point problems

摘要：

针对鞍点问题求解中传统方法收敛速度慢、计算复杂度高的问题，在改进逐次超松弛方法的基础上引人加速因子,提出一种加速MSOR-Like方法,该方法通过优化矩阵分裂与参数控制提升迭代效率与稳定性，并给出收敛性条件.数值实验表明，该方法在迭代步数与计算时间上均优于最优参数的MSOR-Like方法。

To address the issues of slow convergence and high computational complexity in traditional methods for solving saddle point problems, an acelerated MSOR-Like method is proposed by introducing an acceleration factor based on the improved successive over-relaxation approach. This method enhances iteration efficiency and stability through optimized matrix splitting and parameter control. with convergence conditions established. Numerical experiments demonstrate that the proposed method outperforms the optimally parameterized MSOR-Like method in terms of both iteration count and computation time.

作者：

张理涛，朱光旭

Zhang Litao, Zhu Guangxu

机构地区：

郑州航空工业管理学院 a.数学学院；b.航空宇航学院

引用本文：

张理涛，朱光旭。求解特定鞍点问题加速的MSOR-Like方法[J].河南师范大学学报(自然科学版).2026.54(3):60-67. (Zhang Litao,Zhu Guangxu. An accelerated MSOR-Like method for solving specific saddle point problems[J].Journal of Henan Normal University(Natural Science Edition),2026,54(3):60-67.DOI:10.16366/j.cnki.1000-2367.2024.12.18.0002.)

基金：

国家自然科学基金；郑州航院科技创新团队；河南省高等学校重点科研项目计划基础研究专项；河南省校企协同创新项目

关键词：

鞍点问题；收敛性；SOR迭代法；矩阵分裂

saddle point problem; convergence; SOR iterative method; matrix splitting

分类号：

O242

求解特定鞍点问题加速的 MSOR-Like方法.pdf