Solution of systems of nonlinear equations - a semi-implicit approach
2006 (English)Report (Other academic)
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. This relationship enables efficient solution of the Jacobian matrix equations at each iteration. 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 either of the bounding roots makes the method attractive in comparison with methods as those of Newton-Raphson and van Wijngaarden-Dekker-Brent.
Place, publisher, year, edition, pages
Fusion, Plasma and Space Physics
IdentifiersURN: urn:nbn:se:kth:diva-78624OAI: oai:DiVA.org:kth-78624DiVA: diva2:492698
QC 201202272012-02-082012-02-082012-02-27Bibliographically approved