An enhanced matrix-free secant method via predictor-corrector modified line search strategies for solving systems of nonlinear equations
type: Item
instance of: scholarly article
title: An enhanced matrix-free secant method via predictor-corrector modified line search strategies for solving systems of nonlinear equations
zbMATH Open document ID: 1263.65058
DOI: 10.1155/2013/814587
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 2013-05-23T00:00:00Z
review text: Summary: Diagonal updating scheme is among the cheapest Newton-like methods for solving system of nonlinear equations. Nevertheless, the method has some shortcomings. We propose an improved matrix-free secant updating scheme via line search strategies, by using the steps of backtracking in the Armijo-type line search as a step length predictor and Wolfe-Like condition as corrector. Our approach aims at improving the overall performance of diagonal secant updating scheme. Under mild assumptions, the global convergence results have been presented. Numerical experiments verify that the proposed approach is very promising.
Mathematics Subject Classification ID: 65K05
Mathematics Subject Classification ID: 65N30
zbMATH DE Number: 6165372
zbMATH Keywords: nonlinear equations
zbMATH Keywords: Wolfe-Like condition
zbMATH Keywords: global convergence
Wikidata QID: Q58989324
author: M. Y. Waziri
author: Zanariah Abdul Majid
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2013/814587
OpenAlex ID: W2054469474
cites work: Q3702408
cites work: A New Newton's Method with Diagonal Jacobian Approximation for Systems of Nonlinear Equations
cites work: A two-step matrix-free secant method for solving large-scale systems of nonlinear equations
cites work: A Class of Methods for Solving Nonlinear Simultaneous Equations
cites work: Q4841246
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description: scientific article; zbMATH DE number 6165372