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Incomplete Factorizations with S/P and Modified S/P Consistently Ordered M-Factors

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Incomplete Decomposition (ILU) — Algorithms, Theory, and Applications

Part of the book series: Notes on Numerical Fluid Mechanics (NNFM) ((NNFM,volume 29))

Summary

We report here on the first results obtained in the development of a new approximate factorization technique based on the properties of “S/P consistently ordered” M-matrices. An ordered undirected graph is called S/P consistently ordered if whenever a pair of nodes i < j has a common neighbour k with k < i, then either it has also a common neighbour ℓ with j < ℓ or neither i has any neighbour ℓ with ℓ > i nor j any neighbour ℓ with ℓ > j. Incomplete factorizations with (M-matrix) triangular factors whose graphs are S/P consistently ordered have attractive properties which have been analysed. The conclusion of our analysis is that in such cases, the submatrix determined by the nodes without successors should be factored exactly.

The present work was supported by the “Programme d’impulsion en Technologie de l’lnformation” financed by Belgian State, under contract Nr. IT/IF/14.

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Author information

Authors and Affiliations

  1. Service De Métrologie Nucléaire, Université Libre De Bruxelles, C.P. 165, 50, AV. F.D. Roosevelt, B-1050, Brussels, Belgium

    Robert Beauwens

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  1. Robert Beauwens
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Editor information

Editors and Affiliations

  1. Institut für Informatik und Praktische Mathematik, Christian-Albrechts-Universität Kiel, Olshausenstr. 40, W - 2300, Kiel 1, Deutschland

    Wolfgang Hackbusch

  2. IWR, Universität Heidelberg, Im Neuenheimer Feld 368, W - 6900, Heidelberg, Deutschland

    Gabriel Wittum

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

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Beauwens, R. (1993). Incomplete Factorizations with S/P and Modified S/P Consistently Ordered M-Factors. 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_3

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  • DOI: https://doi.org/10.1007/978-3-322-85732-3_3

  • 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

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