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Publication type: Article in scientific journal
Type of review: Peer review (publication)
Title: A global Newton-type scheme based on a simplified Newton-type approach
Authors: Amrein, Mario
et. al: No
DOI: 10.1007/s12190-020-01393-w
Published in: Journal of Applied Mathematics and Computing
Volume(Issue): 65
Issue: 1-2
Pages: 321
Pages to: 334
Issue Date: 9-Jul-2020
Publisher / Ed. Institution: Springer
ISSN: 1598-5865
Language: English
Subjects: Global Newton method; Simplified Newton method; A posteriori analysis; Newton path
Subject (DDC): 510: Mathematics
Abstract: Globalization concepts for Newton-type iteration schemes are widely used when solving nonlinear problems numerically. Most of these schemes are based on a predictor/corrector step size methodology with the aim of steering an initial guess to a zero of f without switching between different attractors. In doing so, one is typically able to reduce the chaotic behavior of the classical Newton-type iteration scheme. In this note we propose a globalization methodology for general Newton-type iteration concepts which changes into a simplified Newton iteration as soon as the transformed residual of the underlying function is small enough. Based on Banach’s fixed-point theorem, we show that there exists a neighborhood around a suitable iterate xn such that we can steer the iterates—without any adaptive step size control but using a simplified Newton-type iteration within this neighborhood—arbitrarily close to an exact zero of f. We further exemplify the theoretical result within a global Newton-type iteration procedure and discuss further an algorithmic realization. Our proposed scheme will be demonstrated on a low-dimensional example thereby emphasizing the advantage of this new solution procedure.
Fulltext version: Published version
License (according to publishing contract): CC BY 4.0: Attribution 4.0 International
Departement: School of Management and Law
Organisational Unit: Institute for Risk & Insurance (IRI)
Appears in collections:Publikationen School of Management and Law

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