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. © 2006 Springer Science + Business Media, Inc.
Higher-order method for the solution of a nonlinear scalar equation / Germani, A.; Manes, C.; Palumbo, P.; Sciandrone, M.. - In: JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS. - ISSN 0022-3239. - 131:3(2006), pp. 347-364. [10.1007/s10957-006-9154-0]
Higher-order method for the solution of a nonlinear scalar equation
Sciandrone M.
2006
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. © 2006 Springer Science + Business Media, Inc.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
