求解一类非线性方程组的Newton-PLHSS方法

J4 ›› 2012, Vol. 47 ›› Issue (12): 96-102.

求解一类非线性方程组的Newton-PLHSS方法

王洋

吉林师范大学数学学院, 吉林四平 136000

收稿日期:2012-02-23 出版日期:2012-12-20 发布日期:2012-12-14
作者简介:王洋(1982- ),女,讲师,博士研究生,研究方向为微分方程数值解.Email: yyang3721@163.com
基金资助:
吉林省自然科学基金资助项目(201115222);吉林师范大学博士启动项目(吉师博2011033)

Newton-PLHSS methods for a class of systems of nonlinear equations

WANG Yang

College of Mathematics, Jilin Normal University, Siping 136000, Jilin, China

Received:2012-02-23 Online:2012-12-20 Published:2012-12-14

摘要/Abstract

摘要：

基于倾向一侧的对称／反对称分裂(LHSS)迭代方法,提出了一类求解Jacobi矩阵在解x*处为大型稀疏非埃尔米特矩阵的非线性方程组的NewtonPLHSS方法,给出了这类不精确牛顿法的两种局部收敛性定理。数值结果验证了该方法的正确性和有效性。

关键词: 对称／反对称分裂;不精确牛顿法;非线性方程组;局部收敛定理

Abstract:

Based on the lopsided Hermitian／skew-Hermitian (LHSS) iteration methods,a class of NewtonPLHSS methods for solving large sparse systems of nonlinear equations with positive definite Jacobi matrices at the solution points is proposed. Two types of local convergence theorems of this class of inexact Newton methods are given. Numerical results confirm the correctness and effectiveness of the proposed methods.

Key words: Hermitian／skew-Hermitian splitting; inexact Newton methods; nonlinear equations; local convergence theorem

王洋. 求解一类非线性方程组的Newton-PLHSS方法[J]. J4, 2012, 47(12): 96-102.

WANG Yang. Newton-PLHSS methods for a class of systems of nonlinear equations[J]. J4, 2012, 47(12): 96-102.

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