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.
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.
About this paper
Journal
Studii şi cercetări matematice
Publisher Name
Academia Republicii S.R.
DOI
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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.
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