一类弱非线性方程组的两参数不精确Picard迭代方法  

ON TWO-PARAMETER INEXACT PICARD ITERATIVE METHODS FOR A CLASS OF WEAKLY NONLINEAR SYSTEMS

作　　者：王洋[1] 伍渝江[2] 

机构地区：[1]吉林师范大学数学学院,四平136000 [2]兰州大学数学与统计学院,兰州730000

出　　处：《高等学校计算数学学报》2014年第4期370-384,共15页Numerical Mathematics A Journal of Chinese Universities

基　　金：国家基础研究规划973项目(2011CB706903);吉林省自然科学基金(201115222);吉林省教育厅十二五科技项目(20130578);吉林师范大学博士启动项目(2011033)

摘　　要：假设矩阵A∈Cn×n为大型稀疏正定矩阵,函数Φ:DCn→Cn为定义在复线性空间Cn的一个开凸子集D上的连续可微函数,且Φ（x）的Jacobi矩阵Φ’（x）在解x*∈D处是非Hermite和负半定的.求解下面的弱非线性代数方程组Ax=Φ（x）,或等价的F（x）:=Ax-Φ（x）=0.（1）For large scale systems of weakly nonlinear equations with separable property of linear and nonlinear terms, by making use of the asymmetric Hermite and skew-Hermite splitting（AHSS） iteration as the inner solver of picard itera- tion, we established two classes of two-parameter inexact Picard iteration methods called Picard-AHSS and nonlinear AHSS-like iteration methods respectively. Un- der suitable conditions, the local convergence theorems for both Picard-AHSS and nonlinear AHSS-like iteration methods are analysis of the convergence theory and the proved. Numerical results confirm the effectiveness of the proposed methods.

关 键 词：nonlinear equations Hermite and skew-Hermite splitting Picard method local convergence property. 

分 类 号：O241.7[理学—计算数学]