Posts by Ion Păvăloiu

Let \(\left( x_{i},\rho_{i}\right) ,\ i=1,2,\) be two complete metric space and \(F_{1}:X_{1}\times X_{2}\rightarrow X_{1},\ F_{2}:X_{1}\times X_{2}\rightarrow X_{2}\) two nonlinear mappings. We study the solving of the system \begin{align}
x_{1} & =F_{1}\left( x_{1},x_{2}\right) \label{f.1}\\
x_{2} & =F_{2}\left( x_{1},x_{2}\right) ,\qquad \left( x_{1},x_{2}\right)
\in X.\nonumber
\end{align} by the Gauss-Seidel type method \begin{align}
x_{1}^{\left( n+1\right) } & =F_{1}\left( x_{1}^{\left( n\right)
},x_{2}^{\left( n\right) }\right) \label{f.2}\\
x_{2}^{\left( n+1\right) } & =F_{2}\left( x_{1}^{\left( n+1\right)
},x_{2}^{\left( n\right) }\right) ,\qquad n=0,1,\ldots;\left( x_{1}^{\left(
0\right) },x_{2}^{\left( 0\right) }\right) \in X\nonumber
\end{align}  We give sufficient conditions for convergence and some error estimations. We also study the case when the mappings \(F_{1}\) and \(F_{2}\) are replaced by some approximations.

Ion Păvăloiu
(Tiberiu Popoviciu Institute of Numerical Analysis)

Original title (in French)

Délimitation des erreur dans la résolution numérique des systèmes d’equations

English translation of the title

Error estimations in the numerical solving of the systems of equations

nonlinear system in metric space; Gauss-Seidel type method; convergence; approximate value

Scanned paper.

PDF-Latex version of the paper.

I. Păvăloiu, Délimitation des erreur dans la résolution numérique des systèmes d’equations, Seminar on mathematical analysis, Preprint no. 7 (1988), pp. 167-178 (in French).

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