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Ljusternik acceleration and the extrapolated S.O.R. method. (English) Zbl 0367.65016


MSC:

65F10 Iterative numerical methods for linear systems
65F15 Numerical computation of eigenvalues and eigenvectors of matrices
65N22 Numerical solution of discretized equations for boundary value problems involving PDEs
65J05 General theory of numerical analysis in abstract spaces
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References:

[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
[2] I. Marek: On a method of accelerating the convergence of iterative processes. Journal Comp. Math. and Math. Phys. 2 (1962), N 2, 963 - 971
[3] I. Marek: On Ljusternik’s method of improving the convergence of nonlinear iterative sequences. Comment. Math. Univ. Carol, 6 (1965), N3, 371 - 380. · Zbl 0195.43003
[4] I. Marek: On some spectral properties of Radon-Nikolskii operators and their generalizations. Comment. Math. Univ. Carol. 3. (1962), N1, 20-30. · Zbl 0119.11403
[5] A. E. Taylor: Introduction to Functional Analysis. J. Wiley Publ. New York, 1958. · Zbl 0081.10202
[6] D. M. Young: Iterative Solution of Large Linear Systems. Academic Press, New York - London, 1971. · Zbl 0231.65034
[7] J. Zítko: Extrapolation of S.O.R. iterations. Apl. Mat. 19 (1974), 72-89.
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