H-矩阵非线性互补问题基于模的矩阵分裂迭代法改进的收敛性定理  

The Improved Convergence Theorems of Modulus-Based Matrix Splitting Iteration Methods for a Class of Nonlinear Complementarity Problems with H-Matrices

作　　者：马昌凤 马飞洋 Ma Changfeng;Ma Feiyang(School of Big Data,Fuzhou University of International Studies and Trade,Fuzhou 350202;School of Electronics Engineering and Computer Science,Peking University,Beijing 100091)

机构地区：[1]福州外语外贸学院大数据学院,福州350202 [2]北京大学信息科学与技术学院,北京100091

出　　处：《数学物理学报（A辑）》2022年第2期583-593,共11页Acta Mathematica Scientia

基　　金：国家自然科学基金(11901098);福建省自然科学基金(2020J05034);国家重点研发计划资助项目(2019YFC03120003)。

摘　　要：该文在较弱的条件下,证明了解一类H-矩阵非线性互补问题基于模的矩阵分裂迭代法和相应的加速迭代法的收敛性定理.这意味着对于分裂A=M-N有更多的选择,使得基于模的矩阵分裂迭代法得以收敛.改进的收敛性定理扩展了基于模的矩阵分裂迭代法的应用范围.In this paper,we proved the convergence theories of the modulus-based matrix splitting iteration methods and the corresponding acceleration method for nonlinear complementarity problems of H-matrices in a weaker condition.It implies that we have more choices for the splitting A=M-N which makes the modulus-based matrix splitting iteration methods converge.The improved convergence theories extend the scope of modulus-based matrix splitting iteration methods in applications.

关 键 词：非线性互补问题 基于模的矩阵分裂迭代法 H-矩阵 收敛性定理 

分 类 号：O241[理学—计算数学]