Maximum-weight-basis preconditioners

نویسندگان

  • Erik G. Boman
  • Doron Chen
  • Bruce Hendrickson
  • Sivan Toledo
چکیده

This paper analyzes a novel method for constructing preconditioners for diagonally-dominant symmetric positivedefinite matrices. The method discussed here is based on a simple idea: we construct M by simply dropping offdiagonal nonzeros from A and modifying the diagonal elements to maintain a certain row-sum property. The preconditioners are extensions of Vaidya’s augmented maximum-spanning-tree preconditioners. The preconditioners presented here were also mentioned by Vaidya in an unpublished manuscript, but without a complete analysis. The preconditioners that we present have only O(n+ t) nonzeros, where n is the dimension of the matrix and t is a parameter that one can choose. Their construction is efficient and guarantees that the condition number of the preconditioned system is O(n/t) if the number of nonzeros per row in the matrix is bounded by a constant. We have developed an efficient algorithm to construct these preconditioners and we have implemented it. We used our implementation to solve a simple model problem; we show the combinatorial structure of the preconditioners and we present encouraging convergence results.

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عنوان ژورنال:
  • Numerical Lin. Alg. with Applic.

دوره 11  شماره 

صفحات  -

تاریخ انتشار 2004