## Highly scalable parallel algorithms for sparse matrix factorization (1994)

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Venue: | IEEE Transactions on Parallel and Distributed Systems |

Citations: | 116 - 29 self |

### BibTeX

@TECHREPORT{Gupta94highlyscalable,

author = {Anshul Gupta and George Karypis and Vipin Kumar},

title = {Highly scalable parallel algorithms for sparse matrix factorization},

institution = {IEEE Transactions on Parallel and Distributed Systems},

year = {1994}

}

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### Abstract

In this paper, we describe a scalable parallel algorithm for sparse matrix factorization, analyze their performance and scalability, and present experimental results for up to 1024 processors on a Cray T3D parallel computer. Through our analysis and experimental results, we demonstrate that our algorithm substantially improves the state of the art in parallel direct solution of sparse linear systems—both in terms of scalability and overall performance. It is a well known fact that dense matrix factorization scales well and can be implemented efficiently on parallel computers. In this paper, we present the first algorithm to factor a wide class of sparse matrices (including those arising from two- and three-dimensional finite element problems) that is asymptotically as scalable as dense matrix factorization algorithms on a variety of parallel architectures. Our algorithm incurs less communication overhead and is more scalable than any previously known parallel formulation of sparse matrix factorization. Although, in this paper, we discuss Cholesky factorization of symmetric positive definite matrices, the algorithms can be adapted for solving sparse linear least squares problems and for Gaussian elimination of diagonally dominant matrices that are almost symmetric in structure. An implementation of our sparse Cholesky factorization algorithm delivers up to 20 GFlops on a Cray T3D for medium-size structural engineering and linear programming problems. To the best of our knowledge,