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An iterative solution method for linear systems of which the coefficient matrix is a symmetric $ M$-matrix

Authors: J. A. Meijerink and H. A. van der Vorst
Journal: Math. Comp. 31 (1977), 148-162
MSC: Primary 65F10
MathSciNet review: 0438681
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Abstract: A particular class of regular splittings of not necessarily symmetric M-matrices is proposed. If the matrix is symmetric, this splitting is combined with the conjugate-gradient method to provide a fast iterative solution algorithm. Comparisons have been made with other well-known methods. In all test problems the new combination was faster than the other methods.

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  • [1] James W. Daniel, The conjugate gradient method for linear and nonlinear operator equations, SIAM J. Numer. Anal. 4 (1967), 10–26. MR 0217987
  • [2] Ky Fan, Note on 𝑀-matrices, Quart. J. Math. Oxford Ser. (2) 11 (1960), 43–49. MR 0117242
  • [3] Magnus R. Hestenes, The conjugate-gradient method for solving linear systems, Proceedings of Symposia in Applied Mathematics. Vol. VI. Numerical analysis, McGraw-Hill Book Company, Inc., New York, for the American Mathematical Society, Providence, R. I., 1956, pp. 83–102. MR 0084178
  • [4] H. S. PRICE & K. H. COATS, "Direct methods in reservoir simulation," Soc. Petroleum Engrs. J., v. 14, 1974, pp. 295-308.
  • [5] J. K. Reid, The use of conjugate gradients for systems of linear equations possessing “Property A”, SIAM J. Numer. Anal. 9 (1972), 325–332. MR 0305567
  • [6] Herbert L. Stone, Iterative solution of implicit approximations of multidimensional partial differential equations, SIAM J. Numer. Anal. 5 (1968), 530–558. MR 0238504
  • [7] Richard S. Varga, Matrix iterative analysis, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1962. MR 0158502
  • [8] Handbook for automatic computation. Vol. II, Springer-Verlag, New York-Heidelberg, 1971. Linear algebra; Compiled by J. H. Wilkinson and C. Reinsch; Die Grundlehren der Mathematischen Wissenschaften, Band 186. MR 0461856
  • [9] J. H. Wilkinson, The algebraic eigenvalue problem, Clarendon Press, Oxford, 1965. MR 0184422

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Article copyright: © Copyright 1977 American Mathematical Society