Multipoint methods for solving nonlinear equations: a survey
Loading...
Authors
Petkovic, Miodrag S.
Neta, Beny
Petkovic, Ljiljana D.
Dzunic, Jovana
Subjects
Nonlinear equations
Iterative methods
Multipoint methods
Computational efficiency
Convergence rate
Acceleration of convergence
Iterative methods
Multipoint methods
Computational efficiency
Convergence rate
Acceleration of convergence
Advisors
Date of Issue
2014
Date
Publisher
Elsevier
Language
Abstract
Multipoint iterative methods belong to the class of the most efficient methods for solving nonlinear equations. Recent interest in the research and development of this type of meth- ods has arisen from their capability to overcome theoretical limits of one-point methods concerning the convergence order and computational efficiency. This survey paper is a mixture of theoretical results and algorithmic aspects and it is intended as a review of the most efficient root-finding algorithms and developing techniques in a general sense. Many existing methods of great efficiency appear as special cases of presented general iter- ative schemes. Special attention is devoted to multipoint methods with memory that use already computed information to considerably increase convergence rate without addi- tional computational costs. Some classical results of the 1970s which have had a great influence to the topic, often neglected or unknown to many readers, are also included not only as historical notes but also as genuine sources of many recent ideas. To a certain degree, the presented study follows in parallel main themes shown in the recently pub- lished book (Petkovic ́ et al., 2013) [53], written by the authors of this paper.
Type
Article
Description
Applied Mathematics and Computation, 226, (2014), 635–640.
The article of record as published may be located at http://dx.doi.org/10.1016/j.amc.2013.10.072
The article of record as published may be located at http://dx.doi.org/10.1016/j.amc.2013.10.072
Series/Report No
Department
Applied Mathematics
Organization
Identifiers
NPS Report Number
Sponsors
Funding
Format
Citation
Distribution Statement
Rights
This publication is a work of the U.S. Government as defined in Title 17, United States Code, Section 101. Copyright protection is not available for this work in the United States.