On the generalized overrelaxation method for operation equations

On the generalized overrelaxation method for operation equations
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Proc. Amer. Math. Soc. 14 (1963), 917-924

DOI: https://doi.org/10.1090/S0002-9939-1963-0169402-2

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References

Julius Albrecht, Fehlerabschätzungen bei Relaxationsverfahren zur numerischen Auflösung linearer Gleichungssysteme, Numer. Math. 3 (1961), 188–201 (German). MR 146957, DOI 10.1007/BF01386019
R. J. Arms, L. D. Gates, and B. Zondek, A method of block iteration, J. Soc. Indust. Appl. Math. 4 (1956), 220–229. MR 119405
George E. Forsythe and Wolfgang R. Wasow, Finite-difference methods for partial differential equations, Applied Mathematics Series, John Wiley & Sons, Inc., New York-London, 1960. MR 0130124
Stanley P. Frankel, Convergence rates of iterative treatments of partial differential equations, Math. Tables Aids Comput. 4 (1950), 65–75. MR 46149, DOI 10.1090/S0025-5718-1950-0046149-3

The iterative solution of elliptic difference equations

Alston S. Householder, On the convergence of matrix iterations, J. Assoc. Comput. Mach. 3 (1956), 314–324. MR 82185, DOI 10.1145/320843.320851

The rate of convergence of the extrapolated Gauss-Seidel iterations

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Herbert B. Keller, On some iterative methods for solving elliptic difference equations, Quart. Appl. Math. 16 (1958), 209–226. MR 117893, DOI 10.1090/S0033-569X-1958-0117893-4
S. G. Kreĭn and O. I. Prozorovskaya, An analogue of Seidel’s method for operator equations, Voronež. Gos. Univ. Trudy Sem. Funkcional. Anal. 5 (1957), 35–38 (Russian). MR 0095579
W. V. Petryshyn, The generalized overrelaxation method for the approximate solution of operator equations in Hilbert space, J. Soc. Indust. Appl. Math. 10 (1962), 675–690. MR 165723
Samuel Schechter, Relaxation methods for linear equations, Comm. Pure Appl. Math. 12 (1959), 313–335. MR 107361, DOI 10.1002/cpa.3160120208
Richard S. Varga, A comparison of the successive overrelaxation method and semi-iterative methods using Chebyshev polynomials, J. Soc. Indust. Appl. Math. 5 (1957), 39–46. MR 90129
David Young, Iterative methods for solving partial difference equations of elliptic type, Trans. Amer. Math. Soc. 76 (1954), 92–111. MR 59635, DOI 10.1090/S0002-9947-1954-0059635-7