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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
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)
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)
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
Young, D.: Iterative solution of large linear systems, Academic Press, New York and London (1971)
Kershaw, D.: The incomplete Cholesky conjugate gradient method for the iterative solution of Systems of linear equations. J. Comput. Phys. 26 (1978), 43–65
Manteuffel, T.A.: The shifted incomplete Cholesky factorization, Technical report, Appl. Math. Division 8325, Sandia Laboratories, Livermore, California, USA (1978)
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)
Gustafsson, I.: On modified incomplete factorizations for a biharmonic problem, in progress
Axelsson, O.: A generalized conjugate direction method and its application on a singular perturbation problem, lecture notes (1979)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1982 Springer-Verlag
About this paper
Cite this paper
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
Download citation
DOI: https://doi.org/10.1007/BFb0064900
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-11970-8
Online ISBN: 978-3-540-39374-0
eBook Packages: Springer Book Archive