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Two-step variants of Richardson’s iterative method. (English. Russian original) Zbl 0657.65049
Cybernetics 23, No. 2, 187-195 (1987); translation from Kibernetika 1987, No. 2, 35-40, 46 (1987).
The author introduces two-step Chebyshev cyclic iterative methods for solving linear systems of algebraic equations. He shows that this method produced simple algorithms which converge faster than the classical Richardson method.
Reviewer: H.Hollatz
65F10 Iterative numerical methods for linear systems
Full Text: DOI
[1] A. Yu. Luchka, O. É. Noshchenko, I. V. Sergienko, and N. I. Tukalevskaya, ?Parallel organization of computations for the solution of linear equations by projective-iterative methods,? Kibernetika, No. 3, 38?47 (1984).
[2] D. K. Faddeev and V. N. Faddeeva, Computational Methods of Linear Algebra, W. H. Freeman, San Francisco (1963). · Zbl 0451.65015
[3] N. S. Bakhvalov, Numerical Methods [in Russian], Nauka, Moscow (1973).
[4] A. V. Buledza, ?To the question of spectral optimization of iterative methods,? Zh. Vychisl. Mat. Mat. Fiz.,22, No. 4, 773?782 (1982). · Zbl 0516.65034
[5] A. A. Samarskii, ?Some topics of general theory of difference schemes,? in: Partial Differential Equations [in Russian], Nauka, Moscow (1970), pp. 191?223.
[6] N. Dunford and J. Schwartz, Linear Operators: General Theory [Russian translation], IL, Moscow (1962).
[7] G. I. Marchuk, Methods of Numerical Mathematics, Springer (1975). · Zbl 0329.65002
[8] G. M. Fikhtengol’ts, A Course of Differential and Integral Calculus [in Russian], Vol. 2, Gostekhizdat, Moscow-Leningrad (1948).
[9] A. A. Samarskii and E. S. Nikolaev, Methods of Solution of Difference Equations [in Russian], Nauka, Moscow (1978). · Zbl 0266.65069
[10] V. I. Lebedev and S. A. Finogenov, ?On one algorithm for parameter choosing in Chebyshev cyclic methods,? in: Computational Methods of Linear Algebra [in Russian], Nauka, Novosibirsk (1972), pp. 21?27.
[11] A. V. Buledza, ?On difference methods for the solution of boundary-value problems for elliptical differential equations,? Differents. Uravn.,1, No. 5, 687?691 (1965).
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