Supernodal Sparse Cholesky Factorization on Distributed-Memory Multiprocessors

Eswar, Kalluri; Sadayappan, P.; Huang, Chua-Huang; Visvanathan, V.

doi:10.1109/icpp.1993.170

Cited by 7 publications

(2 citation statements)

References 5 publications

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“…Ng (1993) considers this case, extending the work of Liu (1987, 1989a) to the supernodal realm. Eswar, Sadayappan, Huang and Visvanathan (1993b) present two distributed-memory supernodal methods (both left-and right-looking), using a one-dimensional distribution of supernodal columns. Large supernodes are split and distributed, as well.…”

Section: Parallel Supernodal Cholesky Factorizationmentioning

confidence: 99%

A survey of direct methods for sparse linear systems

Davis¹,

Rajamanickam²,

Sid-Lakhdar³

2016

Acta Numerica

174

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Wilkinson defined a sparse matrix as one with enough zeros that it pays to take advantage of them.1 This informal yet practical definition captures the essence of the goal of direct methods for solving sparse matrix problems. They exploit the sparsity of a matrix to solve problems economically: much faster and using far less memory than if all the entries of a matrix were stored and took part in explicit computations. These methods form the backbone of a wide range of problems in computational science. A glimpse of the breadth of applications relying on sparse solvers can be seen in the origins of matrices in published matrix benchmark collections (Duff and Reid 1979a, Duff, Grimes and Lewis 1989a, Davis and Hu 2011). The goal of this survey article is to impart a working knowledge of the underlying theory and practice of sparse direct methods for solving linear systems and least-squares problems, and to provide an overview of the algorithms, data structures, and software available to solve these problems, so that the reader can both understand the methods and know how best to use them.

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Section: Parallel Supernodal Cholesky Factorizationmentioning

confidence: 99%

A survey of direct methods for sparse linear systems

Davis¹,

Rajamanickam²,

Sid-Lakhdar³

2016

Acta Numerica

174

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“…These include the fan-out [7], the fanin (basic [l] and compute-ahead [a]), the multzfrontal [SI, the fan-both [3], and the kji-agg-sup [sic] [5] approaches.…”

Section: Previous Workmentioning

confidence: 99%

Memory-adaptive parallel sparse Cholesky factorization

Eswar

Huang

Sadayappan

Proceedings of IEEE Scalable High Performance Computing Conference

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The problem of Cholesky factorization of sparse positive-definite matrices on distributed-memory multiprocessors is considered. A column-based algorithm with the ability to adapt to the amount of memory available on each processor is presented. Exploiting the available memory allows the local computation on each processor to be ordered so that good local eficiencies and dynamic load balance are achieved. A proof that this distributed algorithm is deadlock-free is given. Experimental results of an implementation of this algorithm on an Intel iPSC/SSO multiprocessor system are reported.

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