# On a Steffensen-Hermite method of order three

## Abstract

In this paper we study a third order Steffensen type method obtained by controlling the interpolation nodes in the Hermite inverse interpolation polynomial of degree 2. We study the convergence of the iterative method and we provide new convergence conditions which lead to bilateral approximations for the solution; it is known that the bilateral approximations have the advantage of offering a posteriori bounds of the errors. The numerical examples confirm the advantage of considering these error bounds.

## Authors

Ion Păvăloiu
(Tiberiu Popoviciu Institute of Numerical Analysis, Romanian Academy)

Emil Cătinaş
(Tiberiu Popoviciu Institute of Numerical Analysis, Romanian Academy)

## Keywords

Nonlinear equations; Steffensen type methods; inverse interpolatory polynomials; divided differences.
##### Cite this paper as:

I. Păvăloiu, E. Cătinaş, On a Steffensen-Hermite method of order three, Appl. Math. Comput., 215 (2009) 7, pp. 2663-2672.

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Elsevier

0096-3003

0096-3003