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| Alternate document: Details Parallel Algorithms for Forward and Back Substitution in Direct Solution of Sparse Linear Systems (95) Anshul Gupta, Vipin Kumar |
| Alternate document: Details Parallel Symbolic Computation in ACE (95) Enrico Pontelli, Gopal Gupta |
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Abstract: A few parallel algorithms for solving triangular systems resulting from parallel factorization of sparse linear systems have been proposed and implemented recently. We present a detailed analysis of parallel complexity and scalability of the best of these algorithms and the results of its implementation on up to 256 processors of the Cray T3D parallel computer. It has been a common belief that parallel sparse triangular solvers are quite unscalable due to a high communication to computation... (Update)
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...is used to solve large problems on large number of processors. A few attempts have been made recently to formulate such algorithms [3, 4, 6]. Most of the attempts until now, rely on redistributing the factor matrix from a two dimensional mapping to a one dimensional...
.... on, it has been determined that the stability of this method is only guaranteed if the matrix is well conditioned [11] Gupta and Kumar [9] start from the elimination tree of a Cholesky matrix in order to solve a triangular matrix based on the 2 multifrontal method. In [12]...
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BibTeX entry: (Update)
Anshul Gupta and Vipin Kumar. Parallel algorithms for forward elimination and backward substitution in direct solution of sparse linear systems. In Proc. of Supercomputing'95, December 1995. http://citeseer.ist.psu.edu/gupta95parallel.html More
@inproceedings{ gupta95parallel,
author = "Anshul Gupta and Vipin Kumar",
title = "Parallel Algorithms for Forward and Back Substitution in Direct Solution of Sparse Linear Systems",
pages = "??--??",
year = "1995",
url = "citeseer.ist.psu.edu/gupta95parallel.html" }
Citations (may not include all citations):346 Computer Solution of Large Sparse Positive Definite Systems (context) - George, Liu - 1981
288 Introduction to Parallel Computing: Design and Analysis of A.. (context) - Kumar, Grama et al. - 1994
218 A separator theorem for planar graphs (context) - Lipton, Tarjan - 1979
126 The role of elimination trees in sparse factorization (context) - Liu - 1990
100 Generalized nested dissection (context) - Lipton, Rose et al. - 1979
67 A unified geometric approach to graph separators (context) - Miller, Teng et al. - 1991
59 Isoefficiency: Measuring the scalability of parallel algorit.. (context) - Grama, Gupta et al. - 1993
44 Analyzing scalability of parallel algorithms and architectur.. - Kumar, Gupta - 1994
41 Parallel solution of triangular systems on distributedmemory.. (context) - Heath, Romine - 1988
18 Distributed solution of sparse linear systems - Heath, Raghavan - 1993
15 Communication reduction in parallel sparse Cholesky factoriz.. (context) - George, Liu et al. - 1987
1 Parallel graph partitioning and matrix reordering (context) - Karypis, Kumar - 1995
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