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Alternating direction iteration methods for $ n$ space variables


Authors: J. Douglas, R. B. Kellogg and R. S. Varga
Journal: Math. Comp. 17 (1963), 279-282
MSC: Primary 65.35
DOI: https://doi.org/10.1090/S0025-5718-1963-0160332-7
MathSciNet review: 0160332
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  • [1] Richard S. Varga, Matrix Iterative Analysis, Prentice-Hall, Inc., 1962. MR 0158502 (28:1725)
  • [2] E. G. D'yakonov, ``On a Method of Solving the Poisson Equation,'' Dokl. Akad. Nauk SSSR 143 (1962), 21-24, the same paper appears in English in Soviet Math.-Doklady 3, 1962, p. 320-323. MR 0138205 (25:1652)
  • [3] R. B. Kellogg, ``Another Alternating-Direction-Implicit Method,'' to appear in J. Soc. Ind. Appl. Math. MR 0159414 (28:2631)
  • [4] A. M. Ostrowski, ``Iterative Solution of Linear Systems of Functional Equations,'' J. Math. Anal. Appl., 2, 1961, p. 351-369. MR 0128634 (23:B1672)
  • [5] L. Collatz, ``Fehlerabschätzung für das Iterationsverfahren zur Auflösung linearer Gleichungssysteme,'' Z. Angew. Math. Mech., 22, 1942, p. 357-361. MR 0008714 (5:50b)
  • [6] David G. Feingold, & R. S. Varga, ``Block diagonally dominant matrices and generalizations of the Gerschgorin circle theorem,'' to appear in the Pacific J. Math. MR 0151473 (27:1458)
  • [7] J. Douglas, Jr., and H. H. Rachford, Jr., ``On the numerical solution of heat conduction problems in two or three space variables,'' Trans. Amer. Math. Soc., 82, 1956, p. 421-439. MR 0084194 (18:827f)
  • [8] J. Douglas, Jr., ``Alternating direction methods for three space variables,'' Numer. Math., 4, 1962, p. 41-63. MR 0136083 (24:B2122)

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DOI: https://doi.org/10.1090/S0025-5718-1963-0160332-7
Article copyright: © Copyright 1963 American Mathematical Society

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