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Newton-like method with modification of the right-hand-side vector
Author(s):
Natasa
Krejic;
Zorana
Luzanin.
Journal:
Math. Comp.
71
(2002),
237-250.
MSC (2000):
Primary 65H10
Posted:
May 9, 2001
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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 Obradovica 4, 21000 Novi Sad, Yugoslavia
Email:
natasa@unsim.im.ns.ac.yu
Zorana
Luzanin
Affiliation:
Institute of Mathematics, University of Novi Sad, Trg Dositeja Obradovica 4, 21000 Novi Sad, Yugoslavia
Email:
luzanin@uns.ns.ac.yu
DOI:
10.1090/S0025-5718-01-01322-9
PII:
S 0025-5718(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
Posted:
May 9, 2001
Copyright of article:
Copyright
2001,
American Mathematical Society
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