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https://doi.org/10.21256/zhaw-20601
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DC Field | Value | Language |
---|---|---|
dc.contributor.author | Amrein, Mario | - |
dc.date.accessioned | 2020-10-14T12:37:03Z | - |
dc.date.available | 2020-10-14T12:37:03Z | - |
dc.date.issued | 2020-07-09 | - |
dc.identifier.issn | 1598-5865 | de_CH |
dc.identifier.issn | 1865-2085 | de_CH |
dc.identifier.uri | https://digitalcollection.zhaw.ch/handle/11475/20601 | - |
dc.description.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. | de_CH |
dc.language.iso | en | de_CH |
dc.publisher | Springer | de_CH |
dc.relation.ispartof | Journal of Applied Mathematics and Computing | de_CH |
dc.rights | http://creativecommons.org/licenses/by/4.0/ | de_CH |
dc.subject | Global Newton method | de_CH |
dc.subject | Simplified Newton method | de_CH |
dc.subject | A posteriori analysis | de_CH |
dc.subject | Newton path | de_CH |
dc.subject.ddc | 510: Mathematik | de_CH |
dc.title | A global Newton-type scheme based on a simplified Newton-type approach | de_CH |
dc.type | Beitrag in wissenschaftlicher Zeitschrift | de_CH |
dcterms.type | Text | de_CH |
zhaw.departement | School of Management and Law | de_CH |
zhaw.organisationalunit | Institut für Risk & Insurance (IRI) | de_CH |
dc.identifier.doi | 10.1007/s12190-020-01393-w | de_CH |
dc.identifier.doi | 10.21256/zhaw-20601 | - |
zhaw.funding.eu | No | de_CH |
zhaw.issue | 1-2 | de_CH |
zhaw.originated.zhaw | Yes | de_CH |
zhaw.pages.end | 334 | de_CH |
zhaw.pages.start | 321 | de_CH |
zhaw.publication.status | publishedVersion | de_CH |
zhaw.volume | 65 | de_CH |
zhaw.publication.review | Peer review (Publikation) | de_CH |
zhaw.author.additional | No | de_CH |
zhaw.display.portrait | Yes | de_CH |
Appears in collections: | Publikationen School of Management and Law |
Files in This Item:
File | Description | Size | Format | |
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2020_Amrein_A-global-Newton-type-scheme.pdf | 683.89 kB | Adobe PDF | View/Open |
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Amrein, M. (2020). A global Newton-type scheme based on a simplified Newton-type approach. Journal of Applied Mathematics and Computing, 65(1-2), 321–334. https://doi.org/10.1007/s12190-020-01393-w
Amrein, M. (2020) ‘A global Newton-type scheme based on a simplified Newton-type approach’, Journal of Applied Mathematics and Computing, 65(1-2), pp. 321–334. Available at: https://doi.org/10.1007/s12190-020-01393-w.
M. Amrein, “A global Newton-type scheme based on a simplified Newton-type approach,” Journal of Applied Mathematics and Computing, vol. 65, no. 1-2, pp. 321–334, Jul. 2020, doi: 10.1007/s12190-020-01393-w.
AMREIN, Mario, 2020. A global Newton-type scheme based on a simplified Newton-type approach. Journal of Applied Mathematics and Computing. 9 Juli 2020. Bd. 65, Nr. 1-2, S. 321–334. DOI 10.1007/s12190-020-01393-w
Amrein, Mario. 2020. “A Global Newton-Type Scheme Based on a Simplified Newton-Type Approach.” Journal of Applied Mathematics and Computing 65 (1-2): 321–34. https://doi.org/10.1007/s12190-020-01393-w.
Amrein, Mario. “A Global Newton-Type Scheme Based on a Simplified Newton-Type Approach.” Journal of Applied Mathematics and Computing, vol. 65, no. 1-2, July 2020, pp. 321–34, https://doi.org/10.1007/s12190-020-01393-w.
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