Considerations regarding the iterative methods obtained by inverse interpolation

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

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

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).

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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).

Journal

Studii şi cercetări matematice

Publisher Name

Academia Republicii S.R.

DOI

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Online ISBN

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