Error estimations in the numerical solving of systems of equations in metric spaces

Let \(X_{1},X_{2}\) be two complete metric spaces, \(X=X_{1}\times X_{2}\) and the nonlinear mappings \(F_{1}:X\rightarrow X_{1},\ F_{2}:X\rightarrow X_{2}\). In order to solve the nonlinear system \(x_{1}=F_{1}\left( x_{1},x_{2}\right),\ x_{2}=F_{2}\left( x_{1},x_{2}\right)\) we consider the Gauss-Seidel type method \[x_{n}=F_1 \left(x_{n-1},y_{n-1}\right), \\ y_{n}=F_2 \left( x_{n},y_{n-1}\right) .\] We obtain error estimations when the nonlinear mappings \(F_{1}\) and \(F_{2}\) are approximated by other mappings.

Ion Păvăloiu
(Tiberiu Popoviciu Institute of Numerical Analysis)

Original title (in French)

Estimation des erreurs dans le résolution numérique des systèmes d’équations dans des espaces métriques

English translation of the title

Error estimations in the numerical solving of systems of equations in metric spaces

system of equations in metric space; Gauss-Seidel type method; error estimations

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PDF-Latex version of the paper.

I. Păvăloiu, Estimation des erreurs dans le résolution numérique des systèmes d’équations dans des espaces métriques, Seminar on functional analysis and numerical methods, Preprint no. 1 (1987), pp. 121-129 (in French).

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