求解绝对值方程的两种广义超松弛方法

Two Generalized Successive Overrelaxation Methods for Solving Absolute Value Equations

绝对值方程广泛存在于运筹学、管理科学和工程领域中。对于给定的绝对值方程Ax-|x|=b,其中A为任意实矩阵,提出并分析了求解绝对值方程的广义超松弛(GSOR)方法和改进广义超松弛(MGSOR)方法.此外,研究了这两种方法的收敛性.最后,通过数值实验来验证所提方法的有效性.

Many problems in operations research,management science,and engineering fields lead to solve absolute value equations.In this paper,we suggest and analyze two new methods called generalized successive overrelaxation(GSOR)method and modified generalized successive overrelaxation(MGSOR)method for solving the absolute value equations Ax-|x|=b,where A∈R^(n×n ) is an arbitrary real matrix.Also,we study the convergence properties of the suggested methods.Lastly,we end our paper with numerical examples that show that the given methods are valid and effective for solving absolute value equations.