Abstract
AbstractWe investigate a fast‐convergent derivation‐free method for computing zeros of systems of nonlinear equations with singularities which, in general, needs fewer assumptions than the Newton‐like methods applied usually, and which has proved to be highly efficient by lots of examples. First we transform an arbitrary zero problem into an equivalent, in general under‐determined, zero problem. Then we consider a possibility to transform a zero problem into a possibly globally convergent fixed point form by means of a suitable matrix. We show several possibilities to characterize this matrix. Since the pure Banach iteration provides only linear convergence order of the iterated sequence, we speed up the procedure by means of limit value extrapolation so that we finally obtain a quadratic order of convergence.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
