How good are methods with memory for the solution of nonlinear equations?

How good are methods with memory for the solution of nonlinear equations? 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png SeMA Journal Springer Journals

How good are methods with memory for the solution of nonlinear equations?

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Publisher
Springer Milan
Copyright
Copyright © 2017 by Sociedad Española de Matemática Aplicada (outside the USA)
Subject
Mathematics; Mathematics, general; Applications of Mathematics
ISSN
2254-3902
eISSN
2281-7875
D.O.I.
10.1007/s40324-016-0105-x
Publisher site
See Article on Publisher Site

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.

Journal

SeMA JournalSpringer Journals

Published: Jan 16, 2017

References

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