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A NOTE ON THE PARALLEL CHOLESKY FACTORIZATION OF WIDE BANDED MATRICES

PARALLEL COMPUTING 1989年第2期10卷 239-246页

作者： CONROY, JM UNIV MARYLAND COLLEGE PKMD 20742

In this note, we will describe two algorithms for factoring symmetric positive definite band matrices. Both algorithms are designed for a p × p array of processors with local memory with p ⪕ O (m) , where m is the semibandwidth of the matrix. The p × p model is appropriate for the Ametek Series 2010, which is a mesh, or the popular hypercube architectures, which contain the mesh. Furthermore, the p × p model is studied, since it is the minimal connectivity which is required to implement these algorithms. The first algorithm is achieved by reflecting or folding a systolic array of Brent and Luk. An alternate approach, a torus wrap of the band matrix, is used to give an efficient method which allows the matrix to stay in place during the course of the algorithm. Both algorithms achieve nearly optimal efficiency for matrices whose bandwidth is large relative to the size of the processor array. In fact, their efficiency is asymptotically 1; in lieu of 1/3 efficiency algorithm that can be derived directly from that of Brent and Luk or as presented by Chan et al. We conclude with a medium grain adaptation of these methods, which maintains their near optimality.

关键词： Cholesky factorization parallel linear algebra square array of processors with local memory timing analysis

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