## 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.

Scanned paper.

## 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.