Accelerated iterative methods for finding solutions of a system of nonlinear equations

In this paper, we present a technique to construct iterative methods to approximate the zeros of a nonlinear equation F ( x ) = 0 , where F is a function of several variables. This technique is based on the approximation of the inverse function of F and on the use of a fixed point iteration. Dependi...

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Bibliographic Details
Published in:Applied mathematics and computation 2007-07, Vol.190 (2), p.1815-1823
Main Authors: Grau-Sánchez, Miquel, Peris, Josep M., Gutiérrez, José M.
Format: Article
Language:English
Subjects:
Exact sciences and technology
Global analysis, analysis on manifolds
Iterative methods
Mathematical analysis
Mathematics
Newton’s method
Nonlinear equations
Numerical analysis
Numerical analysis. Scientific computation
Order of convergence
Sciences and techniques of general use
Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds
Zero of a function
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Summary:In this paper, we present a technique to construct iterative methods to approximate the zeros of a nonlinear equation F ( x ) = 0 , where F is a function of several variables. This technique is based on the approximation of the inverse function of F and on the use of a fixed point iteration. Depending on the number of steps considered in the fixed point iteration, or in other words, the number of evaluations of the function F, we obtain some variants of classical iterative processes to solve nonlinear equations. These variants improve the order of convergence of classical methods. Finally, we show some numerical examples, where we use adaptive multi-precision arithmetic in the computation that show a smaller cost.
ISSN:0096-3003
1873-5649
DOI:10.1016/j.amc.2007.02.068