On the multi-point Levenberg-Marquardt method for singular nonlinear equations

被引：7

作者：

Zhao, Xin ^{[1
,2
]}

Fan, Jinyan ^{[1
,2
]}

机构：

[1] Shanghai Jiao Tong Univ, Dept Math, 800 Dongchuan Rd, Shanghai 200240, Peoples R China

[2] Shanghai Jiao Tong Univ, MOE LSC, 800 Dongchuan Rd, Shanghai 200240, Peoples R China

来源：

COMPUTATIONAL & APPLIED MATHEMATICS | 2017年 / 36卷 / 01期

关键词：

Singular nonlinear equations; Levenberg-Marquardt method; Chebyshev's method; Local error bound; OPTIMIZATION SOFTWARE; CONVERGENCE;

D O I：

10.1007/s40314-015-0221-8

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we present a multi-point iterative Levenberg-Marquardt algorithm for singular nonlinear equations. The algorithm converges globally and the convergence order is studied under the local error bound condition, which is weaker than the nonsingularity of the Jacobian at the solution.

引用

页码：203 / 223

页数：21

共 17 条

[1]

[Anonymous], 2001, COMPUTING SUPPLEMENT, DOI DOI 10.1007/978-3-7091-6217-0

[2]

Argyros I., 1993, PROYECCIONES, V12, P119, DOI [10.22199/S07160917.1993.0002.00002, DOI 10.22199/S07160917.1993.0002.00002]

[3] Benchmarking optimization software with performance profiles [J].

Dolan, ED ;

Moré, JJ .

MATHEMATICAL PROGRAMMING, 2002, 91 (02) :201-213

[4] An optimization of Chebyshev's method [J].

Ezquerro, J. A. ;

Hernandez, M. A. .

JOURNAL OF COMPLEXITY, 2009, 25 (04) :343-361

[5]

Fan JY, 2012, MATH COMPUT, V81, P447

[6] On the quadratic convergence of the Levenberg-Marquardt method without nonsingularity assumption [J].

Fan, JY ;

Yuan, YX .

COMPUTING, 2005, 74 (01) :23-39

[7]

Kelley C. T., 1995, ITERATIVE METHODS LI, DOI [10.1137/1.9781611970944, DOI 10.1137/1.9781611970944]

[8]

Kelley Carl T, 2003, SOLVING NONLINEAR EQ, V1, DOI 10.1137/1.9780898718898.ch1

[9]

Levenberg K., 1944, Quarterly of Applied Mathematics, V2, P164, DOI [DOI 10.1090/QAM/10666, 10.1090/QAM/10666]

[10]

Marquardt D., 1963, SIAM J APPL MATH, V11, P431, DOI DOI 10.1137/0111030

← 1 2 →