How good are methods with memory for the solution of nonlinear equations?
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Authors
Chun, Changbum
Neta, Beny
Subjects
Iterative methods with memory
Nonlinear equations
Simple roots
Order of convergence
Basin of attraction
Nonlinear equations
Simple roots
Order of convergence
Basin of attraction
Advisors
Date of Issue
2017
Date
Publisher
Sociedad Española de Matemática Aplicada
Language
Abstract
Multipoint methods for the solution of a single nonlinear equation allow higher order of convergence without requiring higher derivatives. Such methods have an order barrier as conjectured by Kung and Traub. To overcome this barrier, one constructs multipoint methods with memory, i.e. use previously computed iterates. We compare multipoint methods with memory to the best methods without memory and show that the use of memory is computationally more expensive and the methods are not competitive.
Type
Article
Description
The article of record as published may be found at http://dx.doi.org/10.1007/s40324-016-0105-x
Series/Report No
Department
Applied Mathematics
Organization
Naval Postgraduate School (U.S.)
Identifiers
NPS Report Number
Sponsors
National Research Foundation of Korea (NRF), Ministry of Education
Funder
NRF-2016R1D1A1A09917373
Format
13 p.
Citation
C. Chun, B. Neta, "How good are methods with memory for the solution of nonlinear equations?" SeMA, v.74, (2017), pp.613-625.
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.