Journal Article10.1137/0913036
A fast reordering algorithm for parallel sparse triangular solution
Alex Pothen,Fernando L. Alvarado +1 more
TL;DR: A partitioning algorithm that requires only $\mathcal{O}(n)$ time and space for computing an optimal partition, when L is restricted to be a Cholesky factor.
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Abstract: A space-efficient partitioned representation of the inverse of a unit lower triangular matrix L may be used for efficiently solving sparse triangular systems on massively parallel computers. The nu...
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Citations
An Introduction to Chordal Graphs and Clique Trees
Jean R. S. Blair,Barry W. Peyton +1 more
- 01 Jan 1993
TL;DR: In this paper, a unified and elementary introduction to the standard characterizations of chordal graphs and clique trees is presented, as well as a detailed proof of all the results.
A survey of direct methods for sparse linear systems
TL;DR: 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.
254
Fine-Grained Parallel Incomplete LU Factorization
Edmond Chow,Aftab Patel +1 more
TL;DR: Numerical tests show that very few sweeps are needed to construct a factorization that is an effective preconditioner, and the amount of parallelism is large irrespective of the ordering of the matrix, and matrix ordering can be used to enhance the accuracy of the factorization rather than to increase parallelism.
213
Iterative Sparse Triangular Solves for Preconditioning
Hartwig Anzt,Edmond Chow,Jack Dongarra +2 more
- 24 Aug 2015
TL;DR: This work proposes using an iterative approach for solving sparse triangular systems when an approximation is suitable, and demonstrates the performance gains that this approach can have on GPUs in the context of solving sparse linear systems with a preconditioned Krylov subspace method.
An introduction to chordal graphs and clique trees
Jean R. S. Blair,Barry W. Peyton +1 more
- 01 Jan 1993
TL;DR: In this paper, a unified and elementary introduction to the standard characterizations of chordal graphs and clique trees is presented, as well as a detailed proof of all the results.
82
References
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Modification of the minimum-degree algorithm by multiple elimination
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TL;DR: The structural and computation properties of the sparse matrixes encountered in various power system network analysis problems are discussed and the inverses of the factors of sparse matrixe produced by factorization or decomposition are discussed.
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An efficient heuristic ordering algorithm for partial matrix refactorization
TL;DR: An efficient algorithm for ordering a sparse matrix A for partial refactorization and is useful in enhancing the sparsity of the inverse of the triangular factor L and A, and in other applications.
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Partitioned sparse A/sup -1/ methods (power systems)
TL;DR: Tests on practical power system matrices with from 118 to 1993 nodes indicate that the proposed approach is competitive in serial environments, and appears more suitable for parallel environments.