Expanding the Applicability of a Third Order Newton-Type Method Free of Bilinear Operators

被引：0

作者：

Amat, Sergio ^{[1
]}

Busquier, Sonia ^{[1
]}

Bermudez, Concepcion ^{[1
]}

Alberto Magrenan, Angel ^{[2
]}

机构：

[1] Univ Cartagena, Dept Matemat Aplicada & Estadist, Cartagena 21833, Spain

[2] Univ Int La Rioja, Escuela Ingn, C Gran Via 41, Logrono 26005, La Rioja, Spain

来源：

ALGORITHMS | 2015年 / 8卷 / 03期

关键词：

Newton type methods; third order; semilocal convergence; centered hypotheses; divided differences;

D O I：

10.3390/a8030669

中图分类号：

TP18 [人工智能理论];

学科分类号：

081104 ; 0812 ; 0835 ; 1405 ;

摘要：

This paper is devoted to the semilocal convergence, using centered hypotheses, of a third order Newton-type method in a Banach space setting. The method is free of bilinear operators and then interesting for the solution of systems of equations. Without imposing any type of Frechet differentiability on the operator, a variant using divided differences is also analyzed. A variant of the method using only divided differences is also presented.

引用

页码：669 / 679

页数：11

共 35 条

[1] On a third-order Newton-type method free of bilinear operators
Amat, S.
Bermudez, C.
Busquier, S.
Plaza, S.
NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS, 2010, 17 (04) : 639 - 653
[2] ON THE SEMILOCAL CONVERGENCE OF A NEWTON-TYPE METHOD OF ORDER THREE
Argyros, Ioannis K.
Hilout, Said
JOURNAL OF THE KOREAN SOCIETY OF MATHEMATICAL EDUCATION SERIES B-PURE AND APPLIED MATHEMATICS, 2010, 17 (01): : 1 - 27
[3] On a two-step relaxed Newton-type method
Amat, S.
Magrenan, A. A.
Romero, N.
APPLIED MATHEMATICS AND COMPUTATION, 2013, 219 (24) : 11341 - 11357
[4] On a bilinear operator free third order method on Riemannian manifolds
Amat, S.
Argyros, I. K.
Busquier, S.
Castro, R.
Hilout, S.
Plaza, S.
APPLIED MATHEMATICS AND COMPUTATION, 2013, 219 (14) : 7429 - 7444
[5] Third-Order Newton-Type Methods Combined with Vector Extrapolation for Solving Nonlinear Systems
Zhou, Wen
Kou, Jisheng
ABSTRACT AND APPLIED ANALYSIS, 2014,
[6] On two high-order families of frozen Newton-type methods
Amat, S.
Argyros, I.
Busquier, S.
Hernandez-Veron, M. A.
NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS, 2018, 25 (01)
[7] On local convergence of a Newton-type method in Banach space
Argyros, Ioannis K.
Chen, Jinhai
INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS, 2009, 86 (08) : 1366 - 1374
[8] Newton-type methods of high order and domains of semilocal and global convergence
Ezquerro, J. A.
Hernandez, M. A.
Romero, N.
APPLIED MATHEMATICS AND COMPUTATION, 2009, 214 (01) : 142 - 154
[9] Convergence analysis of a variant of Newton-type method for generalized equations
Rashid, M. H.
INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS, 2018, 95 (03) : 584 - 600
[10] On the convergence of extended Newton-type method for solving variational inclusions
Rashid, M. H.
COGENT MATHEMATICS, 2014, 1

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