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On modified incomplete factorization methods

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Numerical Integration of Differential Equations and Large Linear Systems

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 968))

Abstract

In this contribution we present the main theoretical results for the modified incomplete factorization (MIC) methods. For a more detailed study including proofs see [1], where also a more complete list of references can be found. A number of numerical results concerning different classes of problems is included.

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References

  1. Gustafsson, I.: Stability and rate of convergence of modified incomplete Cholesky factorization methods, Report 79.02 R, Department of Computer Sciences, Chalwers University of Technology, Göteborg, Sweden (1979)

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  2. Munksgaard, N.: Solution of general sparse symmetric sets of linear equations, Report No. NI-78-02, Inst. for Num. Anal., Technical University of Denmark, Lyngby, Denmark (1978)

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  3. Meijerink, J.A. and van der Vorst, H.A.: An iterative solution method forlinear systems of which the coefficient matrix is a symmetric M-matrix, Math. Comp. 31 (1977), 148–162

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  4. Young, D.: Iterative solution of large linear systems, Academic Press, New York and London (1971)

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  5. Kershaw, D.: The incomplete Cholesky conjugate gradient method for the iterative solution of Systems of linear equations. J. Comput. Phys. 26 (1978), 43–65

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  6. Manteuffel, T.A.: The shifted incomplete Cholesky factorization, Technical report, Appl. Math. Division 8325, Sandia Laboratories, Livermore, California, USA (1978)

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  7. Axelsson, D. and Gustafsson, I.: A preconditionad conjugate gradient method for finite element equations, which is stable for rounding errors, Report 7924, Mathematisch Institnut, Katholieke Universiteit, Nijmegen, The Netherlands (1979)

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  8. Gustafsson, I.: On modified incomplete factorizations for a biharmonic problem, in progress

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  9. Axelsson, O.: A generalized conjugate direction method and its application on a singular perturbation problem, lecture notes (1979)

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Juergen Hinze

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© 1982 Springer-Verlag

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Gustafsson, I. (1982). On modified incomplete factorization methods. In: Hinze, J. (eds) Numerical Integration of Differential Equations and Large Linear Systems. Lecture Notes in Mathematics, vol 968. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0064900

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  • DOI: https://doi.org/10.1007/BFb0064900

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-11970-8

  • Online ISBN: 978-3-540-39374-0

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