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
(Tiberiu Popoviciu Institute of Numerical Analysis)
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
Cite this paper as:
I. Păvăloiu, Asupra operatorilor iterativi, Studii şi cercetări matematice, 23 10 (1971), pp. 1567-1574 (in Romanian).
About this paper
Journal
Studii şi cercetări matematice
Publisher Name
Academia Republicii S.R.
DOI
Not available yet.
Print ISBN
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Online ISBN
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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.