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.
PDF-LaTeX file (on the journal website).
About this paper
Publisher Name
Article on the journal website
Print ISSN
1222-9024
Online ISSN
2457-8126
MR
1222-9024
Online ISSN
2457-8126
Google Scholar citations
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