Newton-like method with modification of the right-hand-side vector

Authors:
Natasa Krejic and Zorana Luzanin

Journal:
Math. Comp. **71** (2002), 237-250

MSC (2000):
Primary 65H10

Published electronically:
May 9, 2001

MathSciNet review:
1862997

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Abstract | References | Similar Articles | Additional Information

This paper proposes a new Newton-like method which defines new iterates using a linear system with the same coefficient matrix in each iterate, while the correction is performed on the right-hand-side vector of the Newton system. In this way a method is obtained which is less costly than the Newton method and faster than the fixed Newton method. Local convergence is proved for nonsingular systems. The influence of the relaxation parameter is analyzed and explicit formulae for the selection of an optimal parameter are presented. Relevant numerical examples are used to demonstrate the advantages of the proposed method.

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Additional Information

**Natasa Krejic**

Affiliation:
Institute of Mathematics, University of Novi Sad, Trg Dositeja Obradovića 4, 21000 Novi Sad, Yugoslavia

Email:
natasa@unsim.im.ns.ac.yu

**Zorana Luzanin**

Affiliation:
Institute of Mathematics, University of Novi Sad, Trg Dositeja Obradovića 4, 21000 Novi Sad, Yugoslavia

Email:
luzanin@uns.ns.ac.yu

DOI:
https://doi.org/10.1090/S0025-5718-01-01322-9

Keywords:
Nonlinear systems,
Newton method,
chord method

Received by editor(s):
June 22, 1998

Received by editor(s) in revised form:
August 22, 1999, and March 29, 2000

Published electronically:
May 9, 2001

Article copyright:
© Copyright 2001
American Mathematical Society