解奇异非线性方程组的修正张量法  

A MODIFIED TENSOR METHOD FOR SINGULAR NONLINEAR EQUATIONS

作　　者：邱明敏[1] 倪勤[1] 

机构地区：[1]南京航空航天大学数学系,南京210016

出　　处：《南京大学学报（数学半年刊）》2013年第2期253-260,共8页Journal of Nanjing University(Mathematical Biquarterly)

基　　金：国家自然科学基金项目(11071117;11001128)

摘　　要：本文提出解奇异非线性方程组(解点的雅可比矩阵奇异)的修正张量法.修正张量法的主要思想是利用雅可比矩阵的差来构造低秩张量模型,并近似成线性模型来求解.这个修正张量法保持了解奇异问题的超线性收敛性,其计算效果也被部分数值试验结果所证实.In this paper, we propose a modified tensor method for singular nonlinear equations（the Jacobian matrix at the root is singular）. In the modified tensor method, the difference of the Jacobian matrix is used to construct low-rank tensor model, and the approximated linear model is solved. The modified tensor method is superlinearly convergent for solving the singular problems, and its efficiency is showed by some numerical tests.

关 键 词：非线性方程组 修正张量方法 奇异问题 

分 类 号：O241.7[理学—计算数学]