Bitte benutzen Sie diese Kennung, um auf die Ressource zu verweisen:
https://doi.org/10.21256/zhaw-20857| Publikationstyp: | Beitrag in wissenschaftlicher Zeitschrift |
| Art der Begutachtung: | Peer review (Publikation) |
| Titel: | Adaptive Newton-type schemes based on projections |
| Autor/-in: | Amrein, Mario Hilber, Norbert |
| et. al: | No |
| DOI: | 10.1007/s40819-020-00868-5 10.21256/zhaw-20857 |
| Erschienen in: | International Journal of Applied and Computational Mathematics |
| Band(Heft): | 6 |
| Heft: | 120 |
| Erscheinungsdatum: | 2020 |
| Verlag / Hrsg. Institution: | Springer |
| ISSN: | 2199-5796 2349-5103 |
| Sprache: | Englisch |
| Schlagwörter: | Newton-type method; Vector field; Adaptive root finding; Nonlinear equation; Globalization concept; Continuous Newton method |
| Fachgebiet (DDC): | 510: Mathematik |
| Zusammenfassung: | In this work we present and discuss a possible globalization concept for Newton-type methods. We consider nonlinear problems f(x)=0 in Rn using the concepts from ordinary differential equations as a basis for the proposed numerical solution procedure. Thus, the starting point of our approach is within the framework of solving ordinary differential equations numerically. Accordingly, we are able to reformulate general Newton-type iteration schemes using an adaptive step size control procedure. In doing so, we derive and discuss a discrete adaptive solution scheme, thereby trying to mimic the underlying continuous problem numerically without losing the famous quadratic convergence regime of the classical Newton method in a vicinity of a regular solution. The derivation of the proposed adaptive iteration scheme relies on a simple orthogonal projection argument taking into account that, sufficiently close to regular solutions, the vector field corresponding to the Newton scheme is approximately linear. We test and exemplify our adaptive root-finding scheme using a few low-dimensional examples. Based on the presented examples, we finally show some performance data. |
| URI: | https://digitalcollection.zhaw.ch/handle/11475/20857 |
| Volltext Version: | Publizierte Version |
| Lizenz (gemäss Verlagsvertrag): | CC BY 4.0: Namensnennung 4.0 International |
| Departement: | School of Management and Law |
| Organisationseinheit: | Institut für Risk & Insurance (IRI) Institut für Wealth & Asset Management (IWA) |
| Enthalten in den Sammlungen: | Publikationen School of Management and Law |
Dateien zu dieser Ressource:
| Datei | Beschreibung | Größe | Format | |
|---|---|---|---|---|
| 2020_Amrein-Hilber_Adaptive-Newton-type-schemes-based-on-projections.pdf | 1.39 MB | Adobe PDF |  Öffnen/Anzeigen |
Zur Langanzeige
Amrein, M., & Hilber, N. (2020). Adaptive Newton-type schemes based on projections. International Journal of Applied and Computational Mathematics, 6(120). https://doi.org/10.1007/s40819-020-00868-5
Amrein, M. and Hilber, N. (2020) ‘Adaptive Newton-type schemes based on projections’, International Journal of Applied and Computational Mathematics, 6(120). Available at: https://doi.org/10.1007/s40819-020-00868-5.
M. Amrein and N. Hilber, “Adaptive Newton-type schemes based on projections,” International Journal of Applied and Computational Mathematics, vol. 6, no. 120, 2020, doi: 10.1007/s40819-020-00868-5.
AMREIN, Mario und Norbert HILBER, 2020. Adaptive Newton-type schemes based on projections. International Journal of Applied and Computational Mathematics. 2020. Bd. 6, Nr. 120. DOI 10.1007/s40819-020-00868-5
Amrein, Mario, and Norbert Hilber. 2020. “Adaptive Newton-Type Schemes Based on Projections.” International Journal of Applied and Computational Mathematics 6 (120). https://doi.org/10.1007/s40819-020-00868-5.
Amrein, Mario, and Norbert Hilber. “Adaptive Newton-Type Schemes Based on Projections.” International Journal of Applied and Computational Mathematics, vol. 6, no. 120, 2020, https://doi.org/10.1007/s40819-020-00868-5.
Alle Ressourcen in diesem Repository sind urheberrechtlich geschützt, soweit nicht anderweitig angezeigt.