On the computational efficiency index and some iterative methods for solving systems of nonlinear equations

In this paper two new iterative methods are built up and analyzed. A generalization of the efficiency index used in the scalar case to several variables in iterative methods for solving systems of nonlinear equations is revisited. Analytic proofs of the local order of convergence based on developmen...

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Bibliographic Details
Published in:Journal of computational and applied mathematics 2011-10, Vol.236 (6), p.1259-1266
Main Authors: Grau-Sánchez, Miquel, Grau, Àngela, Noguera, Miquel
Format: Article
Language:English
Subjects:
Approximation
Computation
Computational efficiency
Computational efficiency index
Computational order of convergence
Convergence
Iterative methods
Mathematical analysis
Mathematical models
Nonlinear equations
Order of convergence
System of nonlinear equations
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Summary:In this paper two new iterative methods are built up and analyzed. A generalization of the efficiency index used in the scalar case to several variables in iterative methods for solving systems of nonlinear equations is revisited. Analytic proofs of the local order of convergence based on developments of multilineal functions and numerical concepts that will be used to illustrate the analytic results are given. An approximation of the computational order of convergence is computed independently of the knowledge of the root and the necessary time to get one correct decimal is studied in our examples.
ISSN:0377-0427
1879-1778
DOI:10.1016/j.cam.2011.08.008