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Solution of systems of nonlinear equations - a semi-implicit approach
KTH, School of Electrical Engineering (EES), Fusion Plasma Physics.ORCID iD: 0000-0001-6379-1880
KTH, School of Electrical Engineering (EES), Fusion Plasma Physics.
2009 (English)In: Applied Numerical Mathematics, ISSN 0168-9274, E-ISSN 1873-5460, Vol. 59, no 10, 2430-2443 p.Article in journal (Refereed) Published
Abstract [en]

An iterative method for globally convergent solution of nonlinear equations and systems of nonlinear equations is presented. Convergence is quasi-monotonous and approaches second order in the proximity of the real roots. The algorithm is related to semi-implicit methods, earlier being applied to partial differential equations. It is shown that the Newton-Raphson and Newton methods are special cases of the method. The degrees of freedom introduced by the semi-implicit parameters are used to control convergence. When applied to a single equation, efficient global convergence and convergence to a nearby root makes the method attractive in comparison with methods as those of Newton-Raphson and van Wijngaarden-Dekker-Brent. An extensive standard set of systems of equations is solved and convergence diagrams are introduced, showing the robustness, efficiency and simplicity of the method as compared to Newton's method using linesearch.

Place, publisher, year, edition, pages
2009. Vol. 59, no 10, 2430-2443 p.
Keyword [en]
Rootfinding, Root solver, Systems of equations, Iterative methods, Semi-implicit method, Newton's method, Global convergence, large sparse systems
URN: urn:nbn:se:kth:diva-18644DOI: 10.1016/j.apnum.2009.05.002ISI: 000268513700007ScopusID: 2-s2.0-67649774237OAI: diva2:336691
QC 20100525Available from: 2010-08-05 Created: 2010-08-05 Last updated: 2011-01-14Bibliographically approved

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Scheffel, JanHåkansson, Cristian
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