Abstract
Let \(X,Y\) be two normed spaces and \(P:X\rightarrow Y\) a nonlinear operator. We consider the generalized inverse interpolation polynomial and we generalize the Steffensen method. We give some semilocal convergence results and error estimations for the chord method. We also ellaborate a general Steffensen method for which we give the convergence order.
Authors
Ion Păvăloiu
(Tiberiu Popoviciu Institute of Numerical Analysis)
Title
Original title (in Romanian)
Consideraţii asupra metodelor iterative obţinute prin interpolare inversă
English translation of the title
Considerations regarding the iterative methods obtained by inverse interpolation
Keywords
inverse interpolation in normed spaces; nonlinear operator equations; chord method; Steffensen method; semilocal convergence
Cite this paper as:
I. Păvăloiu, Consideraţii asupra metodelor iterative obţinute prin interpolare inversă, Studii şi cercetări matematice, 23 10 (1971), pp. 1545-1549 (in Romanian).
About this paper
Journal
Studii şi cercetări matematice
Publisher Name
Academia Republicii S.R.
DOI
Not available yet.
Print ISBN
Not available yet.
Online ISBN
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References
[1]. Ostrowski, A.M., Reçenie uraunenii i sistem uraunenii. Maskva, 1963.
[2]. Popoviciu, Tiberiu, Sur Ia delimítation de l,erreur dans l’apptroximation des racines d’une
equalions par interpolation linieaire au quadratique. Rev.Roum. de math. pures et appl. XIII, 1 (1968), 75-78.
[3]. Pavaloiu, I., Interpolation dans des espaces linieaires normes et applications. Mathematica, Cluj (sub tipar).