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

Original title (in Romanian)

Asupra operatorilor iterativi

English translation of the title

On iterated operators

Newton method; Traub method; Chord method, convergence order

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Scanned paper.

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

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