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A general semi-iterative acceleration technique is described for improving the convergence of stationary iterative methods. By applying this technique to the successive over relaxation (S.O.R.) iterations with a particular nonoptimal relaxation factor an acceleration of the rate of convergence is obtained which is superior to the optimal S.O.R.
[1] L. A. Ljusternik: A note for the numerical solution of boundary value problems for the Laplace equation and for the calculation of eigenvalues by the method of nets. Trudy Inst. Math. Academy of Sciences of the USSR, 20 (1947), 49-64 (Russian). MR 0025825
[2] I. Marek: On a method of accelerating the convergence of iterative processes. Journal Соmр. Math. and Math. Phys. 2 (1962), N 2, 963 - 971 (Russian). MR 0152112
[3] I. Marek: On Ljusternik's method of improving the convergence of nonlinear iterative sequences. Comment. Math. Univ. Carol, 6 (1965), N3, 371 - 380. MR 0196901
[4] I. Marek: On some spectral properties of Radon-Nikolskii operators and their generalizations. Comment. Math. Univ. Carol. 3. (1962), N1, 20-30. MR 0144216
[5] A. E. Taylor: Introduction to Functional Analysis. J. Wiley Publ. New York, 1958. MR 0098966 | Zbl 0081.10202
[6] D. M. Young: Iterative Solution of Large Linear Systems. Academic Press, New York - London, 1971. MR 0305568 | Zbl 0231.65034
[7] J. Zítko: Extrapolation of S.O.R. iterations. Apl. Mat. 19 (1974), 72-89. MR 0381270
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