# On a third order iterative method for solving polynomial operator equations

## Abstract

We present a semilocal convergence result for a Newton-type method applied to a polynomial operator equation of degree (2).

The method consists in fact in evaluating the Jacobian at every two steps, and it has the r-convergence order at least (3). We apply the method in order to approximate the eigenpairs of matrices.

We perform some numerical examples on some test matrices and compare the method with the Chebyshev method. The norming function we have proposed in a previous paper shows a better convergence of the iterates than the classical norming function for both the methods.

## Authors

Emil Cătinaş
(Tiberiu Popoviciu Institute of Numerical Analysis)

Ion Păvăloiu
(Tiberiu Popoviciu Institute of Numerical Analysis)

## Keywords

nonlinear equations; abstract polynomial equations of degree 2; r-convergence order.

## Cite this paper as:

E. Cătinaş, I. Păvăloiu, On a third order iterative method for solving polynomial operator equations, Rev. Anal. Numér. Théor. Approx., 31 (2002) no. 1, pp. 21-28.

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1222-9024

2457-8126

1222-9024

2457-8126