线性互补问题模系矩阵分裂迭代方法解的扰动分析
Perturbation Analysis of Solutions for Matrix Splitting Iterative Methods of Linear Complementarity Problems
摘要: 线性互补问题在经济，金融，交通和力学等诸多领域有着广泛的应用。因此如何求解结构矩阵线性互补问题的方法已然成为时下数值计算方面的热门话题。而这类问题往往牵涉到大型稀疏矩阵，对于这类问题的解的扰动分析就更加重要。模系矩阵分裂迭代方法是最近提出的用于求解线性互补问题的一种迭代方法，在实际应用中易于实现且非常有效。本文系统地研究了模系矩阵分裂迭代方法下的线性互补问题解的扰动分析，即当系数矩阵发生扰动时，线性互补问题的解作何变化。
Abstract: Linear complementarity problem has been widely used in many fields, such as economy, finance, transportation and mechanics. Therefore, how to solve the linear complementarity problem of structural matrix has become a hot topic in the field of numerical computation. However, this kind of problem often involves large sparse matrices. Splitting iteration method for modular matrix is used for an iterative method for solving the linear complementarity problem is proposed recently; it is easy to implement and is very effective in practical application. This paper systematically stu-dies the modular matrix splitting iterative method, and discusses the method of the linear com-plementarity problem solution of perturbation analysis, namely when the coefficient matrix occurs when the disturbance, the solution for linear complementary changes.
文章引用：何霁, 徐玮玮. 线性互补问题模系矩阵分裂迭代方法解的扰动分析[J]. 应用数学进展, 2018, 7(8): 1040-1046. https://doi.org/10.12677/AAM.2018.78121

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