Results on the effect of orderings on SSOR and ILU preconditionings

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It is known that for SSOR and ILU preconditionings for solving systems of linear equations, orderings can have an enormous impact on robustness, convergence rate and parallelism. Unfortunately, it has been observed that there is an inverse relation between the convergence rate and the parallelism of typical orderings used in practice. This paper presents some numerical experiments with simple matrices to illustrate this behavior as well as a new theoretical result which sheds some light on this phenomenon and also gives an upper bound on the convergence rate of a number of preconditioners in popular use.

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24 pages

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Joubert, W. & Knill, E. December 31, 1998.

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Description

It is known that for SSOR and ILU preconditionings for solving systems of linear equations, orderings can have an enormous impact on robustness, convergence rate and parallelism. Unfortunately, it has been observed that there is an inverse relation between the convergence rate and the parallelism of typical orderings used in practice. This paper presents some numerical experiments with simple matrices to illustrate this behavior as well as a new theoretical result which sheds some light on this phenomenon and also gives an upper bound on the convergence rate of a number of preconditioners in popular use.

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24 pages

Notes

OSTI as DE00348916

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  • Other Information: Supercedes report DE99002488; PBD: [1998]

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  • Other: DE99002488
  • Report No.: LA-UR--98-3841
  • Grant Number: W-7405-ENG-36
  • DOI: 10.2172/348916 | External Link
  • Office of Scientific & Technical Information Report Number: 348916
  • Archival Resource Key: ark:/67531/metadc685604

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Office of Scientific & Technical Information Technical Reports

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  • December 31, 1998

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  • July 25, 2015, 2:20 a.m.

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  • May 5, 2016, 7:20 p.m.

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Joubert, W. & Knill, E. Results on the effect of orderings on SSOR and ILU preconditionings, report, December 31, 1998; New Mexico. (digital.library.unt.edu/ark:/67531/metadc685604/: accessed December 14, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.