求解一类隐式互补问题的加速模系矩阵分裂迭代方法  

Accelerated Modulus-based Matrix Splitting Iteration Method for Solving a Class of Implicit Complementarity Problems

作　　者：黎科良 柯艺芬 马昌凤[1,2,3] LI Keliang;KE Yifen;MA Changfeng(School of Mathematics and Statistics,Fujian Normal University,Fuzhou 350117,China;Fujian Key Laboratory of Mathematical Analysis and Applications,Fuzhou 350117,China;Center for Applied Mathematics of Fujian Province(FJNU),Fuzhou 350117,China)

机构地区：[1]福建师范大学数学与统计学院,福建福州350117 [2]福建省分析数学及应用重点实验室,福建福州350117 [3]福建省应用数学中心,福建福州350117

出　　处：《应用数学》2023年第4期1025-1033,共9页Mathematica Applicata

基　　金：国家自然科学基金资助项目(11901098);福建省自然科学基金(2020J05034)。

摘　　要：本文提出求解一类隐式互补问题的加速模系矩阵分裂迭代法.通过将隐式互补问题重新表述为一个等价的不动点方程,建立一类新的基于模系的两步矩阵分裂方法,并在一定条件下证明了方法的收敛性.数值实验表明,该方法在迭代步数上优于传统的模系矩阵分裂迭代方法.In this paper,a class of accelerated modulus-based matrix splitting iteration method for the implicit complementarity problems is proposed.By reformulating the implicit complementarity problem as an equivalent fixed point equation,a new class of modulus-based two-step matrix splitting methods is established,and its convergence is proved under certain assumptions.Numerical experiments show that this method is superior to the traditional modulus-based matrix splitting iteration methods in the number of iteration steps.

关 键 词：隐式互补问题 基于模系的方法 收敛性 

分 类 号：O242.2[理学—计算数学]