On iterated operators

Abstract

Let \(X,Y\) be normed spaces and \(F:X\rightarrow Y\) a nonlinear operator. Let \(Q:X\rightarrow X.\) We study the convergence orders of iteration operators obtained by composing the given operators. We also study the construction of iterative operators of order \(p+1\), resp. \(2p\), given operators of order \(p\). As particular instances, we consider the Newton, Traub and chord iterative operators.

Authors

Ion Păvăloiu

Title

Original title (in Romanian)

Asupra operatorilor iterativi

English translation of the title

On iterated operators

Keywords

Newton method; Traub method; Chord method, convergence order

References

[1] Janko Bela, Despre rezolvarea ecuatiilor operationale. (Lucrare de Doctorat,  Cluj, 1966).

[2] Pavaloiu Ion, Sur la methode de Steffensen  pour  la resolution des equations operationnelles non lineaires. Rev. Roum de math. pures et appl. 13, 6 (1968), 857-861.

[3] Pavaloiu Ion, Interpolation dans des espaces lineaires norme et applications. Mathematica, Cluj, (sub tipar).

[4] Traub, F. j, Sterative Methods for the solution of equation. Pretince-Holl. Inc. Englewood cliffs. N. j (1964).

[5] Ul’m S., Oboscenie methoda Steffensen dlea resenia nelineinth operatornîh uravnenii. Jurnal vîcise  mat. i mat-fiz. 4, 6 (1964), 1093-1097.

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About this paper

Cite this paper as:

I. Păvăloiu, Asupra operatorilor iterativi, Studii şi cercetări matematice, 23 10 (1971), pp. 1567-1574 (in Romanian).

Journal

Studii şi cercetări matematice

Publisher Name

Academia Republicii S.R.

DOI

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Print ISBN

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Online ISBN

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