| Publication type: | Article in scientific journal |
| Type of review: | Peer review (publication) |
| Title: | An adaptive Newton-method based on a dynamical systems approach |
| Authors: | Amrein, Mario Wihler, Thomas P. |
| et. al: | No |
| DOI: | 10.1016/j.cnsns.2014.02.010 |
| Published in: | Communications in Nonlinear Science and Numerical Simulation |
| Volume(Issue): | 19 |
| Issue: | 9 |
| Page(s): | 2958 |
| Pages to: | 2973 |
| Issue Date: | Sep-2016 |
| Publisher / Ed. Institution: | Elsevier |
| ISSN: | 1007-5704 |
| Language: | English |
| Subjects: | Newton–Raphson method; Continuous Newton–Raphson method; Adaptive step size control; Nonlinear differential equation |
| Subject (DDC): | 510: Mathematics |
| Abstract: | The traditional Newton method for solving nonlinear operator equations in Banach spaces is discussed within the context of the continuous Newton method. This setting makes it possible to interpret the Newton method as a discrete dynamical system and thereby to cast it in the framework of an adaptive step size control procedure. In so doing, our goal is to reduce the chaotic behavior of the original method without losing its quadratic convergence property close to the roots. The performance of the modified scheme is illustrated with various examples from algebraic and differential equations. |
| URI: | https://digitalcollection.zhaw.ch/handle/11475/17926 |
| Fulltext version: | Published version |
| License (according to publishing contract): | Licence according to publishing contract |
| 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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Amrein, M., & Wihler, T. P. (2016). An adaptive Newton-method based on a dynamical systems approach. Communications in Nonlinear Science and Numerical Simulation, 19(9), 2958–2973. https://doi.org/10.1016/j.cnsns.2014.02.010
Amrein, M. and Wihler, T.P. (2016) ‘An adaptive Newton-method based on a dynamical systems approach’, Communications in Nonlinear Science and Numerical Simulation, 19(9), pp. 2958–2973. Available at: https://doi.org/10.1016/j.cnsns.2014.02.010.
M. Amrein and T. P. Wihler, “An adaptive Newton-method based on a dynamical systems approach,” Communications in Nonlinear Science and Numerical Simulation, vol. 19, no. 9, pp. 2958–2973, Sep. 2016, doi: 10.1016/j.cnsns.2014.02.010.
AMREIN, Mario und Thomas P. WIHLER, 2016. An adaptive Newton-method based on a dynamical systems approach. Communications in Nonlinear Science and Numerical Simulation. September 2016. Bd. 19, Nr. 9, S. 2958–2973. DOI 10.1016/j.cnsns.2014.02.010
Amrein, Mario, and Thomas P. Wihler. 2016. “An Adaptive Newton-Method Based on a Dynamical Systems Approach.” Communications in Nonlinear Science and Numerical Simulation 19 (9): 2958–73. https://doi.org/10.1016/j.cnsns.2014.02.010.
Amrein, Mario, and Thomas P. Wihler. “An Adaptive Newton-Method Based on a Dynamical Systems Approach.” Communications in Nonlinear Science and Numerical Simulation, vol. 19, no. 9, Sept. 2016, pp. 2958–73, https://doi.org/10.1016/j.cnsns.2014.02.010.
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