Technical Report CS0665

TR#:CS0665
Class:CS
Title: NEW DIVIDE AND CONQUER PARALLEL ALGORITHMS FOR THE CHOLESKY DECOMPOSITION AND GRAM-SCHMIDT PROCESS
Authors: I. Bar-On
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Abstract: We present a new divide and conquer parallel algorithm for the Cholesky decomposition of dense symmetric positive definite matrices. The decomposition problem is reduced to \ $p$\ independent smaller decomposition problems in \ $log\ p$\ stages. We introduce a new iterative method employing only matrix add and multiply operations for that purpose. The new algorithm offers an \ $O(p)$\ speed-up over the sequential algorithm and can be implemented efficiently on many existing parallel computers. More theoretically, the algorithm runs in \ $O(log^{2}n)$\ time using\ $p = {\cal M}(n)/log^{2}n$\ processors. We conclude with an application to the \ $QR$\ factorization of a full rank matrix.
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