Geodesic
Extrapolation of S. O. R. iterations
Applications of Mathematics, Tome 19 (1974) no. 2, pp. 72-89
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In the paper, the system of $n$ linear algebraic equations $Ax=b$ with 2-cyclic matrix is considered. Methods are derived which converge to the solution $x$ faster than the optimal successive overrelaxation iterative method.
In the paper, the system of $n$ linear algebraic equations $Ax=b$ with 2-cyclic matrix is considered. Methods are derived which converge to the solution $x$ faster than the optimal successive overrelaxation iterative method.
DOI : 10.21136/AM.1974.103516
Classification : 65B05, 65F10, 65J05 
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Zítko, Jan. Extrapolation of S. O. R. iterations. Applications of Mathematics, Tome 19 (1974) no. 2, pp. 72-89. doi: 10.21136/AM.1974.103516

[1] A. S. Householder: The Theory of Matrices in Numerical Analysis. Blaisdell Publishing Company 1965. | MR

[2] D. K. Faddějev, V. N. Faddějevová: Numerical Methods in Linear Algebra. (Numerické metody lineární algebry). SNTL, Praha 1964.

[3] A. Ralston: A First Course in Numerical Analysis. McGraw-Hill Book Company, 1965. | MR | Zbl

[4] R. S. Varga: Matrix Iterative Analysis. Prentice-Hall, Englewood Cliffs, New Jersey 1962. | MR

[5] G. J. Tee: Eigenvectors of the Successive Overrelaxation Process and its Combination with Chebyshev Semi-Iteration. The Computer Journal, Vol. 6, No 3, October 1963, str. 250-263. | DOI

[6] D. M. Young: Iterative Method for Solving Partial Difference Equation of Elliptic Type. Trans. Amer. Math. Soc. 76, 1954, 92-111. | DOI | MR

[7] E. Humhal J. Zítko: Contribution to the S.O.R. Method. (Poznámka k superrelaxační metodě). Aplikace matematiky 3, sv. 12, 1967, 161 - 170. | MR

[8] Л. А. Люстерник: Замечания к численному решению краевых задач уравнения Лапласа и вычислениям собственных значений методом сеток. Tp. Матем. института АН СССР, 1947, 20, 49-64. | MR | Zbl

[9] I. Marek: On Ljusternik's Method of Improving Convergence of Nonlinear Iterative Sequences. CMUC 6, 3, 1965, 371-380. | MR

[10] И. Марек: Об одном методе ускорения сходимости итерационных процесов. ЖВМиМФ, Том 2, Но 6, 1962, 963-971. | MR | Zbl

[11] С. G. Broyden: Some Generalizations of the Theory of Successive Over-Relaxation. Numer. Math. 6, Heft 4, 1964, 269-284. | DOI | MR

[12] L. A. Hageman R. B. Kellogg: Estimating Optimum Overrelaxation Parameter. Math. of Соmр., January 1968, Vol. 22, No 101, 60-68. | MR

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