Higher-Order Method for the Solution of a Nonlinear Scalar Equation

A. Germani, C. Manes, P. Palumbo and M. Sciandrone ()
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A. Germani: University of L’Aquila
C. Manes: University of L’Aquila
P. Palumbo: Istituto di Analisi dei Sistemi ed Informatica A. Ruberti, CNR
M. Sciandrone: Istituto di Analisi dei Sistemi ed Informatica A. Ruberti, CNR

Journal of Optimization Theory and Applications, 2006, vol. 131, issue 3, No 3, 347-364

Abstract: Abstract A new iterative method to find the root of a nonlinear scalar function f is proposed. The method is based on a suitable Taylor polynomial model of order n around the current point x k and involves at each iteration the solution of a linear system of dimension n. It is shown that the coefficient matrix of the linear system is nonsingular if and only if the first derivative of f at x k is not null. Moreover, it is proved that the method is locally convergent with order of convergence at least n + 1. Finally, an easily implementable scheme is provided and some numerical results are reported.

Keywords: Root-finding algorithms; Newton method; higher-order methods; order of convergence (search for similar items in EconPapers)
Date: 2006
References: View complete reference list from CitEc
Citations: View citations in EconPapers (3)

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DOI: 10.1007/s10957-006-9154-0

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