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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
DOI: https://doi.org/10.1090/S0025-5718-01-01322-9
Published electronically: May 9, 2001
MathSciNet review: 1862997
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Abstract:

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

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