# On some interpolatory iterative methods for the second degree polynomial operators (I)

## Abstract

In this note we consider the chord (secant) method and the Steffensen method for solving polynomial operators of degree 2 on Banach spaces, $$F:X\rightarrow Y$$.

The convergence conditions in this case are simplified, as the divided difference of order 3 is the null trilinear operator.

As particular cases, we study the eigenproblem for quadratic matrices and integral equations of Volterra type.

We obtain semilocal convergence results, which show the r-convergence orders of the iterates.

## Authors

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

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

## Keywords

chord/secant method; Steffensen method; polynomial operator equation of degree 2 on Banach spaces; divided differences; eigenproblem for quadratic matrices; integral equations of Volterra type; semilocal convergence; r-convergence order.

## Cite this paper as:

E. Cătinaş, I. Păvăloiu, On some interpolatory iterative methods for the second degree polynomial operators (I), Rev. Anal. Numér. Théor. Approx., 27 (1998) no. 1, pp. 33-45.

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##### Publisher Name

Editions de l’Academie Roumaine

1222-9024

2457-8126

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