Some variant of Newton's method with third-order convergence

Authors:
M. Frontini;E. Sormani
Affiliations:
Dipartimento di Matematica, Piazza Leonardo da Vinci Politecnico di Milano, Piazza Leonardo da Vinci 32, I-20133 Milano, Italy;Dipartimento di Matematica, Piazza Leonardo da Vinci Politecnico di Milano, Piazza Leonardo da Vinci 32, I-20133 Milano, Italy
Venue:
Applied Mathematics and Computation
Year:
2003

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Abstract

We present a new modification of the Newton's method which produces iterative methods with order of convergence three. A general error analysis providing the higher order of convergence is given, and the best efficiency, in term of function evaluations, of two of this new methods is provided.