Sur quelques méthodes itératives pour la résolution des équations opérationnelles

On some iterative methods for solving operational equations

Authors

  • A. Diaconu Tiberiu Popoviciu Institute of Numerical analysis, Romanian Academy, Romania
  • I. Păvăloiu Tiberiu Popoviciu Institute of Numerical Analysis, Romanian Academy, Romania

DOI:

https://doi.org/10.33993/jnaat11-3
Abstract views: 309

Abstract

Let \(X,Y\) be two Banach spaces and \(P:X\rightarrow Y\) a nonlinear operator. We study the semilocal convergence of the Newton, chord and Steffensen methods for which the derivative \(P^{\prime}\left( x\right) \) or the divided differences from each iteration step are approximated by a sequence of operators obtained with the Schultz method:
\begin{equation}
\left\{
\begin{array}
[c]{l}%
x_{n+1}=x_{n}-A_{n}P\left( x_{n}\right) \\
A_{n+1}=A_{n}\left( 2E-\left[ x_{n},x_{n+1};P\right] A_{n}\right)
,\qquad n=0,1,\ldots
\end{array}
\right. \label{f.1.6}%
\end{equation}
and considering the Steffensen method:%
\begin{equation}
\left\{
\begin{array}
[c]{l}%
x_{n+1}=x_{n}-A_{n}P\left( x_{n}\right) \\
A_{n+1}=A_{n}\left( 2E-\left[ x_{n+1},Q\left( x_{n+1}\right) ;P\right]
A_{n}\right) ,\qquad n=0,1,\ldots
\end{array}
\right. \label{f.1.7}%
\end{equation}

MR0381294 (52 #2191)

Zbl 0363.65046

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References

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Published

1972-02-01

How to Cite

Diaconu, A., & Păvăloiu, I. (1972). Sur quelques méthodes itératives pour la résolution des équations opérationnelles: On some iterative methods for solving operational equations. Rev. Anal. Numér. Théorie Approximation, 1, 45–61. https://doi.org/10.33993/jnaat11-3

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