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Numerische Mathematik

, Volume 13, Issue 5, pp 377–395 | Cite as

A generalisation of systematic relaxation methods for consistently ordered matrices

  • P. J. Taylor
Article

Summary

A systematic relaxation method is analysed for consistently ordered matrices as defined by Broyden (1964). The method is a generalisation of successive over-relaxation (S.O.R.). A relation is derived between the eigenvalues of the iteration matrix of the method and the eigenvalues of the Jacobi iteration matrix. Forp-cyclic matrices, the method corresponds to using a special type of diagonal matrix instead of a single relaxation factor. For certain choices of this diagonal matrix, the method has a better asymptotic rate of convergence than S.O.R. and requires less calculations and computer store.

Keywords

Mathematical Method Diagonal Matrix Relaxation Method Relaxation Factor Iteration Matrix 
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References

  1. Broyden, C. G.: Some generalisations of the theory of successive over-relaxation. Num. Math.6, 269–284 (1964).Google Scholar
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  3. Tee, G. J.: An application ofp-cyclic matrices for solving periodic parabolic problems. Num. Math.6, 142–159 (1964).Google Scholar
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Copyright information

© Springer-Verlag 1969

Authors and Affiliations

  • P. J. Taylor
    • 1
  1. 1.Department of MathematicsThe University SouthamptonGreat Britain

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