Advertisement

A new approximate factorization method

  • Yvan Notay
Chapter
Part of the Notes on Numerical Fluid Mechanics (NNFM) book series (NNFM, volume 29)

Summary

A new incomplete factorization method is presented, differing from the previous ones by the way in which the diagonal entries of the triangular factors are defined. A comparison is given with other basic incomplete factorization methods, displaying the superiority of the new one, particularly for systems arising from anisotropic elliptic PDEs.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    O. Axelsson, A generalized SSOR method ,BIT, 13 (1972), pp. 443–467.CrossRefMathSciNetGoogle Scholar
  2. [2]
    O. Axelsson, On iterative solution of elliptic difference equations on a mesh connected array of processors ,J. High Speed Comput., 1 (1989), pp. 165–184.CrossRefzbMATHGoogle Scholar
  3. [3]
    O. Axelsson an. V. Barker Finite Element Solution of Boundary Value Problems. Theory and Computation ,Academic Press, New York, 1984.zbMATHGoogle Scholar
  4. [4]
    O. Axelsson an. G. Lindskog On the eigenvalue distribution of a class of preconditioning methods ,Numer. Math., 48 (1986), pp. 479–498.CrossRefzbMATHMathSciNetGoogle Scholar
  5. [5]
    R. BEAUWENS, Lower eigenvalue bounds for pencils of matrices ,Lin. Alg. Appl., 85 (1987), pp. 101–119.CrossRefzbMATHMathSciNetGoogle Scholar
  6. [6]
    R. BeauWENS, Modified incomplete factorization strategies , in Preconditioned Conjugate Gradient Methods, O. Axelsson and L. Kolotilina, eds., Lectures Notes in Mathematics No. 1457, Springer-Verlag, 1990, pp. 1–16.Google Scholar
  7. [7]
    R. BEAUWENS AND R. WlLMET, Conditioning analysis of positive definite matrices by approximate factorizations ,J. Comput. Appl. Math., 26 (1989), pp. 257–269.CrossRefzbMATHMathSciNetGoogle Scholar
  8. [8]
    I. GUSTAFSSON, Modified Incomplete Cholesky (MIC) methods , in Preconditioning Methods. Theory and Applications, D. Evans, ed., Gordon and Breach, New York-London-Paris, 1983, pp. 265–293.Google Scholar
  9. [9]
    Y. NOTAY, Incomplete factorization of singular linear systems ,BIT, 29 (1989), pp. 682–702.CrossRefzbMATHMathSciNetGoogle Scholar
  10. [10]
    Y. NOTAY, Solving positive (semi)definite linear systems by preconditioned iterative methods , in Preconditioned Conjugate Gradient Methods, O. Axelsson and L. Kolotilina, eds., Lectures Notes in Mathematics No. 1457, Springer-Verlag, 1990, pp. 105–125.CrossRefGoogle Scholar
  11. [11]
    Y. NOTAY, Resolution iterative de systèmes linéaires par factorisations approchées ,PhD thesis, Service de Métrologie Nucléaire, Université Libre de Bruxelles, Brussels, Belgium, 1991.Google Scholar
  12. [12]
    Y. NOTAY, Upper eigenvalue bounds and related modified incomplete factorization strategies , in Iterative Methods in Linear Algebra, R. Beauwens and P. de Groen, eds., North-Holland, 1992, pp. 551–562.Google Scholar
  13. [13]
    Y. NOTAY, On the robustness of modified incomplete factorization methods ,Inter. J. Comp. Math., to appear, (1991).Google Scholar
  14. [14]
    Y. NOTAY, On the convrgence rate of the conjugate gardients in presence of rounding errors ,Numer. Math., submitted, (1991).Google Scholar
  15. [15]
    Y. NOTAY, A dynamic version of the RIC method ,submitted for publication.Google Scholar
  16. [16]
    H. VAN DER VORST, The convergence behaviour of preconditioned CG and CG-S , in Preconditioned Conjugate Gradient Methods, O. Axelsson and L. Kolotilina, eds., Lectures Notes in Mathematics No. 1457, Springer-Verlag, 1990, pp. 126–136.CrossRefGoogle Scholar
  17. [17]
    G. WlTTUM, On the robustness of ILU-smoothing ,SIAM J. Sci. Statist. Comput., 10 (1989), pp. 699–717.CrossRefMathSciNetGoogle Scholar

Copyright information

© Friedr. Vieweg & Sohn Verlagsgesellschaft mbH, Braunschweig/Wiesbaden 1993

Authors and Affiliations

  • Yvan Notay
    • 1
  1. 1.Service de Métrologie NucléaireUniversité Libre de BruxellesBrusselsBelgium

Personalised recommendations