On the Nonmonotone Behavior of the Newton-Gmback Method

Journal Article · Wed Sep 17 00:00:00 EDT 2008 · AIP Conference Proceedings

DOI:https://doi.org/10.1063/1.2997323· OSTI ID:21251378

Catinas, Emil ^[1]

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1. Romanian Academy, 'T. Popoviciu' Institute of Numerical Analysis, P.O. Box 68-1, Cluj-Napoca (Romania)

GMBACK is a Krylov solver for large linear systems, which is based on backward error minimization properties. The minimum backward error is guaranteed (in exact arithmetic) to decrease when the subspace dimension is increased. In this paper we consider two test problems which lead to nonlinear systems which we solve by the Newton-GMBACK. We notice that in floating point arithmetic the mentioned property does not longer hold; this leads to nonmonotone behavior of the errors, as reported in a previous paper. We also propose a remedy, which solves this drawback.

• OSTI ID: 21251378
• Journal Information: AIP Conference Proceedings, Vol. 1046, Issue 1; Conference: ICNAAM-2007: International conference on numerical analysis and applied mathematics 2007; ICCMSE-2007: International conference on computational methods in sciences and engineering 2007, Corfu (Greece), 16-20 Sep 2007; 25-30 Sep 2007; Other Information: DOI: 10.1063/1.2997323; (c) 2008 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); ISSN 0094-243X
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICAL METHODS AND COMPUTING
99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE
ERRORS
MATHEMATICAL SOLUTIONS
MINIMIZATION
NEWTON METHOD
NONLINEAR PROBLEMS