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A study of the method of approximate factorization for solving grid elliptic boundary-value problems

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References

  1. A. B. Kucherov and M. M. Makarov, Difference Methods in Mathematical Physics [in Russian], Izd. Mosk. Gos. Univ., Moscow (1984).

    Google Scholar 

  2. A. B. Kucherov and M. M. Makarov, Numerical Methods for Solving Problems of Mathematical Physics [in Russian], Izd. Mosk. Gos. Univ., Moscow (1986).

    Google Scholar 

  3. A. A. Samarskii, Theory of Difference Schemes [in Russian], Nauka, Moscow (1977).

    Google Scholar 

  4. A. A. Samarskii and E. S. Nikolaev, Methods for Solving Grid Equations [in Russian], Nauka, Moscow (1978).

    Google Scholar 

  5. T. Dupont, R. Kendall, and H. H. Rachford, “An approximate factorization procedure for solving self-adjoint elliptic difference equations,” SIAM, J. Numer. Anal.,5, 559–573 (1968).

    Google Scholar 

  6. O. Axelsson, “A generalized SSOR method,” BIT,13, 443–467 (1972).

    Google Scholar 

  7. I. Gustafsson, “A class of first-order factorization method,” BIT,18, 142–156 (1974).

    Google Scholar 

  8. R. Beauwens, “Lower eigenvalue bounds for pencils of matrices,” Lin. Alg. Appl.,85, 101–119 (1987).

    Google Scholar 

  9. I. Gustafsson, “On modified incomplete Cholesky factorization methods for the solution of problems with mixed boundary conditions and problems with discontinuous material coefficients,” Int. J. Numer. Meth. Eng.,14, 1127–1140 (1979).

    Google Scholar 

  10. R. Beauwens, “Approximate factorizations with S/P consistently ordered M-factors,” BIT,29, 658–681 (1989).

    Google Scholar 

  11. V. V. Kucherenko and G. A. Trunov, “On the rate of convergence of methods of approximate factorization,” Mat. Zametki,46, No. 5, 29–39 (1989).

    Google Scholar 

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Translated from Matematicheskie Zametki, Vol. 54, No. 3, pp. 72–88, September, 1993.

The authors would like to express sincere gratitude to A. A. Samarskii for consistent attention to this work and for his useful discussion.

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Kucherov, A.B., Makarov, M.M. A study of the method of approximate factorization for solving grid elliptic boundary-value problems. Math Notes 54, 923–933 (1993). https://doi.org/10.1007/BF01209557

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