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On the successive over-relaxation method for cyclic operators. (English) Zbl 0096.32303


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[1] Frankel, S.: Convergence rates of iterative treatments of partial differential equations. MTAC4, 65-75 (1950).
[2] Young, D.: Iterative methods for solving partial difference equations of elliptic type. Doctoral thesis, Harvard University, 1950.
[3] Carlsson, S. G., andA. Elldin: Solving equations of state in telephone traffic theory with digital computers. Ericsson Technics 1958, 221-244.
[4] Kjellberg, G.: On the convergence of successive over-relaxation applied to a class of linear systems of equations with complex eigen-values. Ericsson Technics 1958, 245-258.
[5] Arms, L. J., L. D. Gates andB. Zondek: A method of block iteration. J. SIAM4, 220-229 (1956).
[6] Young, D.: Iterative methods for solving partial difference equations of elliptic type. Trans. Amer. Math. Soc.76, 92-111 (1954). · Zbl 0055.35704
[7] Frobenius, G.: Über Matrizen aus nicht negativen Elementen. Sitz.-Ber. Akad. Wiss. Berlin, 1912, 456-477. · JFM 43.0204.09
[8] Romanovsky, V.: Recherches sur les chaines deMarkoff. Acta Math.66, 147-251 (1936). · Zbl 0014.02802
[9] Varga, R. S.:P-cyclic matrices: a generalization of the Young-Frankel successive overrelaxation scheme. Report WAPD-T-567 of the Bettis Plant of the Westinghouse Electric Corporation, August 1957. · Zbl 0088.09402
[10] Varga, R. S.:P-cyclic matrices: a generalization of the Young-Frankel successive overrelaxation scheme. Pacific J. Math.9, 617-628 (1959). · Zbl 0088.09402
[11] Kjellberg, G.: A generalization ofYoung’s theorem on the successive overrelaxation method. Proc. of the International Conf. on Information Processing, Paris 1959. Unesco 1960.
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