Empirically modified block incomplete factorizations

  • Magolu monga-Made
Part of the Notes on Numerical Fluid Mechanics (NNFM) book series (NNFM, volume 29)


Dynamic variants of modified block incomplete factorization with modulated additive perturbations have been introduced recently and found to be superior to the standard block methods, in particular when applied to difficult problems for which the usual modified version gives rise to strongly isolated largest eigenvalues. We show here that in the case where the PDE coefficients are strongly anisotropic, care should be taken to provide some enough selection of the perturbed nodes in order to avoid a severe loss of efficiency.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    O. AXELSSON, On the eigenvalue distribution of relaxed incomplete factorization methods and the rate of convergence of conjugate gradient methods ,Technical Report, Departement of Mathematics, Catholic University, Nijmegen, The Netherlands, 1989.Google Scholar
  2. [2]
    O. AXELSSON AND V. BARKER, Finite Element Solution of Boundary Value Problems. Theory and Computation ,Academic Press, New York, 1984.zbMATHGoogle Scholar
  3. [3]
    O. AXELSSON AND G. LlNDSKOG, On the eigenvalue distribution of a class of preconditioning methods ,Numer. Math., 48 (1986), pp. 479–498.CrossRefzbMATHMathSciNetGoogle Scholar
  4. [4]
    R. BEAUWENS, Lower eigenvalue bounds for pencils of matrices ,Lin. Alg. Appl., 85 (1987), pp. 101–119.CrossRefzbMATHMathSciNetGoogle Scholar
  5. [5]
    R. BEAUWENS AND M. BEN BOUZID, Existence and conditioning properties of sparse approximate block factorizations ,SIAM J. Numer. Anal., 25 (1988), pp. 941–956.CrossRefzbMATHMathSciNetGoogle Scholar
  6. [6]
    A. BEN ISRAEL AND T.N.E. GREVILLE, Generalized Inverses : Theory &Applications ,J. Wiley &Sons, New York, 1974.Google Scholar
  7. [7]
    A. GREENBAUM, Behavior of slightly perturbed lanczos and conjugate-gradient recurrences ,Lin. Alg. Appl., 113 (1989), pp. 7–63.CrossRefzbMATHMathSciNetGoogle Scholar
  8. [8]
    M.M. MAGOLU, Conditioning analysis of sparse block approximate factorizations ,Appl. Numer. Math., 8 (1991), pp. 25–42.CrossRefzbMATHMathSciNetGoogle Scholar
  9. [9]
    M.M. MAGOLU, Analytical bounds for block approximate factorization methods ,(1992), Lin. Alg. Appl. To appear.Google Scholar
  10. [10]
    M.M. MAGOLU, Modified block-approximate factorization strategies ,Numer. Math. 61 (1992), pp. 91–110.CrossRefzbMATHMathSciNetGoogle Scholar
  11. [11]
    M.M. MAGOLU, Lower eigenvalue bounds for singular pencils of matrices ,(1992), J. Comput. Appl. Math. To appear.Google Scholar
  12. [12]
    M.M. MAGOLU, Sparse block approximate factorizations for singular problems , in Iterative Methods in Linear Algebra, R. Beauwens and P. de Groen, eds., North-Holland, 1992.Google Scholar
  13. [13]
    M.M. MAGOLU, Sparse approximate block factorizations for solving symmetric positive (semi)definite linear systems ,thèse de Doctorat, Université Libre de Bruxelles, Brussels, Belgium, 1992.Google Scholar
  14. [14]
    M.M. MAGOLU AND Y. NOTAY, On the conditioning analysis of block approximate factorization methods ,Lin. Alg. Appl., 154–156 (1991), pp. 583–599.CrossRefMathSciNetGoogle Scholar
  15. [15]
    Y. NOTAY, Polynomial acceleration of iterative schemes associated with subproper splittings ,J. Comput. Appl. Math., 24 (1988), pp. 153–167.CrossRefzbMATHMathSciNetGoogle Scholar
  16. [16]
    Y. NOTAY, Resolution iterative de systèmes linéaires par factorisations approchées ,thèse de Doctorat, Université Libre de Bruxelles, Brussels, Belgium, 1991.Google Scholar
  17. [17]
    Y. NOTAY, Conditioning analysis of modified block incomplete factorizations ,Lin. Alg. Appl., 154–156 (1991), pp. 711–722.CrossRefMathSciNetGoogle Scholar
  18. [18]
    A. VAN DER Sluis, The convergence behaviour of conjugate gradients and ritz values in various circumstances , in Iterative Methods in Linear Algebra, R. Beauwens and P. de Groen, eds., North-Holland, 1992.Google Scholar
  19. [19]
    H.A. 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

Copyright information

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

Authors and Affiliations

  • Magolu monga-Made
    • 1
  1. 1.Service de Métrologie NucléaireUniversité Libre de BruxellesBrusselsBelgium

Personalised recommendations