广义绝对值方程组的局部预条件类SOR方法  

A Local Preconditioned SOR-like Method for Generalized Absolute Value Equations

作　　者：张珍珠 李朝迁[2] ZHANG Zhenzhu;LI Chaoqian(School of Mathematics and Computer Science,Hanjiang Normal University,Shiyan 442000;School of Mathematics and Statistics,Yunnan University,Kunming 650504)

机构地区：[1]汉江师范学院数学与计算机科学学院,十堰442000 [2]云南大学数学与统计学院,昆明650504

出　　处：《工程数学学报》2025年第1期45-58,共14页Chinese Journal of Engineering Mathematics

基　　金：国家自然科学基金(12061087)。

摘　　要：广义绝对值方程组在经济、工程等领域有着重要作用,其求解已成为计算数学和优化方向的重要问题之一。基于广义绝对值方程组的等价形式及预条件技术,对求解广义绝对值方程组的高效算法进行了研究,提出了局部预条件类SOR迭代法,讨论了该方法的收敛性,并通过数值算例说明了该方法在某些情况下优于已有方法。Generalized absolute value equations play an important role in fields such as Economics and Engineering,and solving it has become one of the important problems in computational mathematics and optimization.Based on their equivalent forms and preconditioning techniques,we have conducted research on efficient algorithms for solving generalized absolute value equations,a local preconditioned SOR-like method is proposed.The convergence of this method is discussed.Numerical examples are also given to demonstrate that it outperforms some existing methods in some cases.

关 键 词：广义绝对值方程组 预条件 SOR迭代法 类SOR法 

分 类 号：O241.7[理学—计算数学]