|Title:||EFFICIENT LOGARITHMIC TIME PARALLEL ALGORITHMS FOR THE CHOLESKY DECO~OSITION OF BAND MATRICES
|Abstract:||We present a parallel algorithm for finding the Cholcsky decomposition of a band symmetric positive definite matrix of order n and bandwidth m in 0(nm2 /p) time using p ~ (n/m)/Iog(n/m) processors. Furthermore, there are only O(log p) interprocessor conununication phases, and the operation count is only as twice as that of the sequential algorithm. We conclude that the algorithm can be efficiently implemented 011 existing parallel computers. We also consider the general bandwidth case and show that the algolithm can be implemented in O(log m log n) time using p = nm2/(log m log n) processors, with at most o(log2p) interprocessor communication phases.|
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