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https://doi.org/10.21256/zhaw-20601| 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 10.21256/zhaw-20601 |
| 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 1865-2085 |
| 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. |
| URI: | https://digitalcollection.zhaw.ch/handle/11475/20601 |
| 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 |
Files in This Item:
| File | Description | Size | Format | |
|---|---|---|---|---|
| 2020_Amrein_A-global-Newton-type-scheme.pdf | 683.89 kB | Adobe PDF |  View/Open |
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