On the efficiency of two variants of Kurchatov’s method for solving nonlinear systems

We consider Kurchatov’smethod and construct two variants of this method for solving systems of nonlinear equations and deduce their local R -orders of convergence in a direct symbolic computation. We also propose a generalization to several variables of the efficiency used in the scalar case and ana...

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Bibliographic Details
Published in:Numerical algorithms 2013-12, Vol.64 (4), p.685-698
Main Authors: Ezquerro, José Antonio, Grau, Angela, Grau-Sánchez, Miquel, Ángel Hernández, Miguel
Format: Article
Language:English
Subjects:
Algebra
Algorithms
Computer Science
Nonlinear equations
Nonlinear systems
Numeric Computing
Numerical Analysis
Original Paper
Theory of Computation
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Summary:We consider Kurchatov’smethod and construct two variants of this method for solving systems of nonlinear equations and deduce their local R -orders of convergence in a direct symbolic computation. We also propose a generalization to several variables of the efficiency used in the scalar case and analyse the efficiencies of the three methods when they are used to solve systems of nonlinear equations.
ISSN:1017-1398
1572-9265
DOI:10.1007/s11075-012-9685-4