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two step extrapolation; optimum choice of relaxation factor; convergence acceleration; successive overrelaxation; iterative process; S.O.R. method
Limits of the extrapolation coefficients are rational functions of several poles with the largest moduli of the resolvent operator $R(\lambda, T)=(\lambda I -T)^{-1}$ and therefore good estimates of these poles could be calculated from these coefficients. The calculation is very easy for the case of two coefficients and its practical effect in finite dimensional space is considerable. The results are used for acceleration of S.O.R. method.
[1] J. Zítko: Improving the convergence of iterative methods. Apl. Mat. 28 (1983), 215-229. MR 0701740
[2] J. Zítko: Convergence of extrapolation coefficients. Apl. Mat. 29 (1984), 114-133. MR 0738497
[3] J. Zítko: Extrapolation of iterative processes. Rostock. Math. Kolloq. 25, 63-78 (1984). MR 0763678
[4] I. Marek J. Zítko: Ljusternik acceleration and the extrapolated S.O.R. method. Appl. Mat. 22 (1977), 116-133. MR 0431667
[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] R. S. Varga: Matrix Iterative Analysis. Prentice-Hall, Englewood Cliffs, New Jersey 1962. MR 0158502
[8] G. Maess: Extrapolation bei Iterationsverfahren. ZAMM 56 (1976), 121-122. DOI 10.1002/zamm.19760560210 | MR 0426417
[9] G. Maess: Iterative Lösung linearer Gleichungssysteme. Deutsche Akademie der Naturforscher Leopoldina Halle (Saale), 1979. MR 0558164 | Zbl 0416.65029
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