Sparse Cholesky factorization on a local-memory multiprocessor
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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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Abstract: This article deals with the problem of factoring a large sparse positive definite matrix on a multiprocessor system. The processors are assumed to have substantial local memory but no globally shared memory. They communicate among themselves and with a host processor through message passing. Our primary interest is in designing an algorithm which exploits parallelism, rather than in exploiting features of the underlying topology of the hardware. However, part of our study is aimed at determining, for certain sparse matrix problems, whether hardware based on the binary hypercube topology adequately supports the communication requirements for such problems. Numerical results from experiments conducted on a hypercube multiprocessor are included.
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Citations
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Developments and trends in the parallel solution of linear systems
Iain S. Duff,Henk A. van der Vorst +1 more
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TL;DR: This review paper considers some important developments and trends in algorithm design for the solution of linear systems concentrating on aspects that involve the exploitation of parallelism and considers preconditioning techniques for iterative solvers.
References
Modification of the minimum-degree algorithm by multiple elimination
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A New Implementation of Sparse Gaussian Elimination
TL;DR: An implementation of sparse ${LDL}^T$ and LU factorization and back-substitution, based on a new scheme for storing sparse matrices, is presented and appears to be as efficient in terms of work and storage as existing schemes.
227
Parallel implementation of multifrontal schemes
Iain S. Duff
- 20 Jul 1986
TL;DR: This work considers the direct solution of large sparse sets of linear equations in an MIMD environment using a multifrontal approach and shows how to distribute tasks among processors according to an elimination free that can be automatically generated from any pivot strategy.
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