Technical Report CS0665

TR#:CS0665
Class:CS
Title: NEW DIVIDE AND CONQUER PARALLEL ALGORITHMS FOR THE CHOLESKY DECOMPOSITION AND GRAM-:SCHMIDT PROCESS
Authors: Llan Bar-On
PDFCS0665.pdf
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(log2n) tiine using p = M(n)/log2n processors. We conclude with an application to the QR factorization of a full rank matrix.

Key words. Cholesky decomposition, Gram-Schmidt process, QR factorization, iterative methods, parallel algorithms.

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