High order algorithms for approximating nth roots

Abstract

In this article, by means of a modification of the Newton method, we obtain a family of iterative processes which approximates the nth root of a real number with a prefixed order of convergence q, q ≥ 2.

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Keywords:

• Iterative processes
• Order of convergence
• Semilocal convergence
• n th Root

Acknowledgement

Supported in part by a grant from the DGES (Ref. BFM 2002-00222) and a grant from the University of La Rioja (Ref. API-02/18).

Notes

E-mail: [email protected]