非线性方程组的非交替Newton-PHSS迭代法  

Non-alternating Newton-PHSS iteration method for systems of nonlinear equations

作　　者：伍渝江[1] 陈亮[1] 

机构地区：[1]兰州大学数学与统计学院,兰州730000

出　　处：《应用数学与计算数学学报》2017年第2期153-162,共10页Communication on Applied Mathematics and Computation

基　　金：国家自然科学基金资助项目(11471150)

摘　　要：大型稀疏非Hermite正定Jacobi矩阵对应的非线性方程组的迭代求解历来受到重视.结合不精确Newton法和非交替PHSS迭代法,提出了迭代求解非线性方程组的NewtonNPHSS方法,给出了迭代法的局部收敛定理,并演算了数值例子,阐明了Newton-NPHSS是有效的迭代法.Much attention has been paid on the iteration solution for large scale and sparse systems of nonlinear equations whose Jacobian matrix is non-Hermitian positive definite during these years. Our goal in this paper is to combine the inexact Newton method with non-alternating preconditioned Hermitian and skew- Hermitian splitting （PHSS） iteration method, and to present a non-alternating Newton-PHSS （Newton-NPHSS） iteration method for solving systems of nonlinear equations. Local convergence theorem of the method is given. Numerical examples are carried out to verify the effectiveness of Newton-NPHSS method.

关 键 词：非线性方程组 不精确NEWTON法 Newton-HSS法 局部收敛 

分 类 号：O241.7[理学—计算数学]