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.
The present work was supported by the “Programme d’impulsion en Technologie de l’lnformation”, financed by Belgian State, under contract No. IT/IF/14.
Supported by the “Fonds National de la Recherche Scientifique”, Charge de recherches.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
O. Axelsson, A generalized SSOR method ,BIT, 13 (1972), pp. 443–467.
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.
O. Axelsson an. V. Barker Finite Element Solution of Boundary Value Problems. Theory and Computation ,Academic Press, New York, 1984.
O. Axelsson an. G. Lindskog On the eigenvalue distribution of a class of preconditioning methods ,Numer. Math., 48 (1986), pp. 479–498.
R. BEAUWENS, Lower eigenvalue bounds for pencils of matrices ,Lin. Alg. Appl., 85 (1987), pp. 101–119.
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.
R. BEAUWENS AND R. WlLMET, Conditioning analysis of positive definite matrices by approximate factorizations ,J. Comput. Appl. Math., 26 (1989), pp. 257–269.
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.
Y. NOTAY, Incomplete factorization of singular linear systems ,BIT, 29 (1989), pp. 682–702.
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.
Y. NOTAY, Resolution iterative de systèmes linéaires par factorisations approchées ,PhD thesis, Service de Métrologie Nucléaire, Université Libre de Bruxelles, Brussels, Belgium, 1991.
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.
Y. NOTAY, On the robustness of modified incomplete factorization methods ,Inter. J. Comp. Math., to appear, (1991).
Y. NOTAY, On the convrgence rate of the conjugate gardients in presence of rounding errors ,Numer. Math., submitted, (1991).
Y. NOTAY, A dynamic version of the RIC method ,submitted for publication.
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.
G. WlTTUM, On the robustness of ILU-smoothing ,SIAM J. Sci. Statist. Comput., 10 (1989), pp. 699–717.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1993 Friedr. Vieweg & Sohn Verlagsgesellschaft mbH, Braunschweig/Wiesbaden
About this chapter
Cite this chapter
Notay, Y. (1993). A new approximate factorization method. In: Hackbusch, W., Wittum, G. (eds) Incomplete Decomposition (ILU) — Algorithms, Theory, and Applications. Notes on Numerical Fluid Mechanics (NNFM), vol 29. Vieweg+Teubner Verlag, Wiesbaden. https://doi.org/10.1007/978-3-322-85732-3_11
Download citation
DOI: https://doi.org/10.1007/978-3-322-85732-3_11
Publisher Name: Vieweg+Teubner Verlag, Wiesbaden
Print ISBN: 978-3-528-07641-2
Online ISBN: 978-3-322-85732-3
eBook Packages: Springer Book Archive