On iterated operators


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.


Ion Păvăloiu
(Tiberiu Popoviciu Institute of Numerical Analysis)


Original title (in Romanian)

Asupra operatorilor iterativi

English translation of the title

On iterated operators


Newton method; Traub method; Chord method, convergence order


Cite this paper as:

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

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Studii şi cercetări matematice

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Academia Republicii S.R.


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[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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