## Abstract

In this paper we give a condition for the convergence of an iterative method of Gauss-Seidel type \[ x_i = \varphi (x_{i-1}, y_{i-1}) \\ y_i = \psi (x_i, y_{i-1})\] for solving the nonlinear system of equations of the type: \[ x = \varphi (x, y) \\ y = \psi (x, y). \] We then provide some error evaluations in case of exact and approximate computations. We also provide a sufficient condition when the system contains \(k\) equations with \(k\) unknowns \[x_i = \varphi_i (x_1,x_2,…,x_k), \quad i=1,…,k.\]

## Authors

Ion Păvăloiu – Tiberiu Popoviciu Institute of Numerical Analysis

## Title

### Original Title (in Romanian)

Observații asupra rezolvării sistemelor de ecuații cu ajutorul procedeelor iterative

### English Translation of the Title

Remarks on solving the systems of equations by iterative methods

## Keywords

nonlinear system of equations; fixed point problem; Gauss-Seidel method.

## References

- B.P. Demidovici, I.A. Maron,
*Osnovi vacislietel’noi matematiki,*Gas. izd. fiz. mat. lit., Moskva, 1960, pp. 148–151. - J.F. Traub,
*Iterative Methods for the Solution of Equations*. Prentice Hall, Inc., Englewwod Cliffs, N.J., 1964, 99.38-39. - A.M. Ostrowski,
*Resenie uravnenii i sistem uravnenii,*Izd. inostr. lit., Moskva, 1963, pp. 83–94. - I. Pavaloiu,
*On some recurrent inequalities and some of their applications*, Communication at the Scientific Session of the Institute for Mining Petrosani, February 7–10, 1966.

## About this paper

##### Cite this paper as:

I. Păvăloiu, *Observaţii asupra rezolvării sistemelor de ecuaţii cu ajutorul procedeelor iterative*, Studii şi cercetări matematice, **19** (1967) no. 9, pp. 1289-1298.

##### Journal

Studii şi cercetări matematice

##### Publisher Name

Academia Republicii S.R.

##### DOI

Not available yet.

##### MSC

Not available yet.

##### MR

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##### ZBL

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