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Analysis of a recursive 5-point/9-point factorization method

  • O. Axelsson
  • V. Eijkhout
Submitted Papers
Part of the Lecture Notes in Mathematics book series (LNM, volume 1457)

Abstract

Nested recursive two-level factorization methods for nine-point difference matrices are analyzed. Somewhat similar in construction to multilevel methods for finite element matrices, these methods use recursive red-black orderings of the meshes, approximating the nine-point stencils by five-point ones in the red points and then forming the reduced system explicitly. As this Schur complement is again a nine-point matrix (on a skew grid this time), the process of approximating and factorizing can be applied anew.

Progressing until a sufficiently coarse grid has been reached, this gives a multilevel preconditioner for the original matrix. Solving the levels in V-cycle order will not give an optimal order method, but we show that using certain combinations of V-cycles and W-cycles will give methods of both optimal order of numbers of iterations and computational complexity.

Keywords

Algebraic multilevel Chebyshev polynomial approximation nine-point differences optimal order preconditioners 

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Copyright information

© Springer-Verlag 1990

Authors and Affiliations

  • O. Axelsson
    • 1
  • V. Eijkhout
    • 1
  1. 1.Department of MathematicsUniversity of Nijmegenthe Netherlands

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