Journal Article10.1137/0911033
A Fan-In Algorithm for Distributed Sparse Numerical Factorization
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TL;DR: A column-oriented distributed algorithm for factoring a large sparse symmetric positive definite matrix on a local-memory parallel processor that achieves good speedups on an Intel iPSC/2 hypercube.
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Abstract: This paper presents a column-oriented distributed algorithm for factoring a large sparse symmetric positive definite matrix on a local-memory parallel processor. Processors cooperate in computing each column of the Cholesky factor by calculating independent updates to the corresponding column of the original matrix. These updates are sent in a fan-in manner to the processor assigned to the column, which then completes the computation. Experimental results on an Intel iPSC/2 hypercube demonstrate that the method is effective and achieves good speedups.
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Citations
Direct methods for sparse matrices
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SPOOLES: An Object-Oriented Sparse Matrix Library.
Cleve Ashcraft,Roger G. Grimes +1 more
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133
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TL;DR: Progress in the use of direct methods for solving very large sparse symmetric positive definite systems of linear equations on vector supercomputers is summarized.
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TL;DR: This article deals with the problem of factoring a large sparse positive definite matrix on a multiprocessor system where the processors are assumed to have substantial local memory but no globally shared memory.
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Charles H Romine,James M. Ortega +1 more
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