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Optimization of the Relaxation Parameter for S.S.O.R. and A.D.I. Preconditioning

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Abstract

We present and compare several approaches for the optimization of the relaxation parameter both for A.D.I. and S.S.O.R. basic iteration and preconditioning conjugate gradient method. For each kind of preconditioning a detailed link between estimates of the spectral radius of the iteration matrix and of the condition number resulting from preconditioning is proposed. It allows to choose the best approach in order to obtain the optimal relaxation parameter and the corresponding optimal estimates either of the spectral radius of the iteration matrix and of the resulting condition mumber of the S.S.O.R. and A.D.I. preconditioning.

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Authors and Affiliations

  1. Département de Mathématiques, UFR Sciences et Techniques, 16 route de Gray, F-25030, Besancon Cedex, France

    J.C. Miellou

  2. ENSEEIHT-IRIT/LIMA, 2 rue Camichel, B.P. 7122, F-31 071, Toulouse Cedex, France

    P. Spiteri

Authors
  1. J.C. Miellou
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  2. P. Spiteri
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Miellou, J., Spiteri, P. Optimization of the Relaxation Parameter for S.S.O.R. and A.D.I. Preconditioning. Numerical Algorithms 29, 153–195 (2002). https://doi.org/10.1023/A:1014876410019

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