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

共 50 条

[41] COMPARING THE LOCAL CONVERGENCE ANALYSIS OF SOME NEWTON-LIKE METHODS FOR SOLVING EQUATIONS
Argyros, Ioannis K.
Shrestha, Nirjal
ADVANCES AND APPLICATIONS IN MATHEMATICAL SCIENCES, 2018, 17 (07): : 503 - 518
[42] Local convergence analysis of inexact Newton-like methods under majorant condition
O. P. Ferreira
M. L. N. Gonçalves
Computational Optimization and Applications, 2011, 48 : 1 - 21
[43] PRECONDITIONED INEXACT NEWTON-LIKE METHOD FOR LARGE NONSYMMETRIC EIGENVALUE PROBLEMS
Miao, Hong-Yi
Wang, Li
NUMERICAL ALGEBRA CONTROL AND OPTIMIZATION, 2021, 11 (04): : 677 - 685
[44] Families of Newton-like methods with fourth-order convergence
Jain, Divya
INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS, 2013, 90 (05) : 1072 - 1082
[45] CONCERNING THE RADII OF CONVERGENCE FOR A CERTAIN CLASS OF NEWTON-LIKE METHODS
Argyros, Ioannis K.
JOURNAL OF THE KOREAN SOCIETY OF MATHEMATICAL EDUCATION SERIES B-PURE AND APPLIED MATHEMATICS, 2008, 15 (01): : 47 - 55
[46] Newton-like methods for solving vector optimization problems
Lu, Fang
Chen, Chun-Rong
APPLICABLE ANALYSIS, 2014, 93 (08) : 1567 - 1586
[47] The convergence ball of Newton-like methods in Banach space and applications
Chen, Jinhai
Sun, Qingying
TAIWANESE JOURNAL OF MATHEMATICS, 2007, 11 (02): : 383 - 397
[48] CONVERGENCE OF NEWTON-LIKE METHODS FOR SOLVING SYSTEMS OF NONLINEAR EQUATIONS
BUS, JCP
NUMERISCHE MATHEMATIK, 1977, 27 (03) : 271 - 281
[49] A CLASS OF NEWTON-LIKE METHODS WITH CUBIC CONVERGENCE FOR NONLINEAR EQUATIONS
Ye, Qiaojun
Xu, Xiubin
FIXED POINT THEORY, 2010, 11 (01): : 161 - 168
[50] On the convergence of newton-like methods under general and unifying conditions
Argyros, Ioannis K.
Gutierrez, Jose M.
FIXED POINT THEORY AND APPLICATIONS, VOL 6, 2007, 6 : 7 - +

← 1 2 3 4 5 →