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

Abstract

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.

Authors

Ion Păvăloiu

Title

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

Keywords

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

References

[1] Pavaloiu, I., La resolution des systemes operationnelles a l’aide des methodes iteratives, Mathematica, 11(34), 1969, 137–141.

[2] Urabe, M., Error estimation in numerical solution of equation by iteration processes, J. Sci. Hiroshima Univ., Ser. A-I, 26 (1962), 77–91.

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About this paper

Cite this paper as:

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).

Journal

Seminar on functional analysis and numerical methods,
Preprint

Publisher Name

“Babes-Bolyai” University,
Faculty of Mathematics and Physics,
Research Seminars

DOI

Not available yet.

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