Abstract
Let \(X\) be a Banach space and \(Y\) a normed space, and \(P:X\rightarrow Y\) a nonlinear operator. In order to solve the equation \(P\left( x\right)=0\), we consider the iterative method \(x_{n+1}=x_{n}+\varphi \left(x_{n}\right) \), where \(\varphi:X\rightarrow X\). We give some sufficient semilocal conditions relating \(\varphi\) and \(P\) for these iterations to converge to a solution with a given convergence order. As particular instances, we obtain convergence results for the Newton, Chebyshev and Steffensen mehods.
Authors
Ion Păvăloiu
(Tiberiu Popoviciu Institute of Numerical Analysis)
Title
Original title (in French)
Sur les procedées itératifs à un ordre élevé de convergence
English translation of the title
On the iterative methods with high convergence orders
Keywords
iterative methods in normed spaces; convergence order; Newton type method; Chebyshev type method; Steffensen type method; semilocal convergence
Cite this paper as:
I. Păvăloiu, Sur les procedées itérative à un order élevé de convergence, Mathématica, 12(35) (1970) no. 2, pp. 309-324 (in French).
About this paper
Journal
Mathematica
Publisher Name
Academia Republicii S.R.
DOI
Not available yet.
Print ISBN
Not available yet.
Online ISBN
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References
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