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.
Scanned paper: on the journal website.
Latex version of the paper (soon).
About this paper
Publisher Name
Editions de l’Academie Roumaine
Article on the journal website
Print ISSN
1222-9024
Online ISSN
2457-8126
MR
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ZBL
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Google Scholar citations
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