CONVERGENCE ANALYSIS OF NEWTON-LIKE METHODS FOR INVERSE EIGENVALUE PROBLEMS WITH MULTIPLE EIGENVALUES

被引：7

作者：

Shen, Weiping ^{[1
]}

Li, Chong ^{[2
]}

Yao, Jen-Chih ^{[3
]}

机构：

[1] Zhejiang Normal Univ, Dept Math, Jinhua 321004, Peoples R China

[2] Zhejiang Univ, Sch Math Sci, Hangzhou 310027, Zhejiang, Peoples R China

[3] China Med Univ, Ctr Gen Educ, Taichung 40402, Taiwan

来源：

SIAM JOURNAL ON NUMERICAL ANALYSIS | 2016年 / 54卷 / 05期

基金：

中国国家自然科学基金;

关键词：

nonlinear equation; inverse eigenvalue problem; Newton's method; Newton-like method;

D O I：

10.1137/15M1049063

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We provide in the present paper a corrected proof for the classical quadratical convergence theorem (i.e., Theorem 3.3 in Friedland, Nocedal, and Overton [SIAM T. Numer. Anal., 24 (1987), pp. 634-667]) of the Newton-like method for solving inverse eigenvalue problems with possible multiple eigenvalues. Moreover, as a by-product, our approach developed here can be extended to establish a similar convergence result for an inexact version of the Newton-like method with possible multiple eigenvalues, which is an extension of the corresponding inexact Newton-like method for the distinct case in Chan, Chung, and Xu [BIT Numer. Math., 43 (2003), pp. 7-20].

引用

页码：2938 / 2950

页数：13

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