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 xk 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 xk 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.

A higher order method for the solution of nonlinear scalar equations

GERMANI, Alfredo;MANES, COSTANZO;
2006-01-01

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 xk 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 xk 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.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11697/7784
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