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Abstract: We have developed a highly parallel sparse Cholesky factorization algorithm that 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. However, it had been a challenge to developing efficient and scalable parallel formulations of sparse matrix factorization. Our new... (Update)
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BibTeX entry: (Update)
@misc{ gupta-scalable,
author = "Anshul Gupta",
title = "Scalable Parallel Algorithms for Solving Sparse Systems of Linear Equations",
url = "citeseer.ist.psu.edu/345931.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
222 A fast multilevel implementation of recursive spectral bisec.. - Barnard, Simon - 1992
218 A separator theorem for planar graphs (context) - Lipton, Tarjan - 1979
195 Department of Computer Science - Speelpening, element et al. - 1978
126 The multifrontal solution of indefinite sparse symmetric lin.. (context) - Duff, Reid - 1983
126 The role of elimination trees in sparse factorization (context) - Liu - 1990
110 Nested dissection of a regular finite-element mesh (context) - George - 1973
100 Generalized nested dissection (context) - Lipton, Rose et al. - 1979
73 Parallel algorithms for dense linear algebra computations (context) - Gallivan, Plemmons et al. - 1990
59 Isoefficiency: Measuring the scalability of parallel algorit.. (context) - Grama, Gupta et al. - 1993
51 Sparse Cholesky factorization on a local memory multiprocess.. (context) - George, Heath et al. - 1988
45 An efficient block-oriented approach to parallel sparse Chol.. (context) - Rothberg, Gupta - 1992
44 Analyzing scalability of parallel algorithms and architectur.. - Kumar, Gupta - 1994
43 Massively parallel methods for engineering and science probl.. - Camp, Plimpton et al. - 1994
41 Task scheduling for parallel sparse Cholesky factorization (context) - Geist, Ng - 1989
41 Parallel solution of triangular systems on distributed-memor.. (context) - Heath, Romine - 1988
33 A parallel solution method for large sparse systems of equat.. (context) - Lucas, Blank et al. - 1987
33 A fan-in algorithm for distributed sparse numerical factoriz.. (context) - Ashcraft, Eisenstat et al. - 1990
32 Parallel multilevel graph partitioning - Karypis, Kumar - 1995
29 Communication results for parallel sparse Cholesky factoriza.. (context) - George, Liu et al. - 1989
29 Efficient parallel solution of linear systems (context) - Pan, Reif - 1985
28 Towards a fast implementation of spectral nested dissection (context) - Pothen, Simon et al. - 1992
24 Highly parallel sparse Cholesky factorization - Gilbert, Schreiber - 1992
23 Users' guide for the Harwell-Boeing sparse matrix collection - Duff, Grimes et al. - 1992
23 Performance properties of large scale parallel systems - Gupta, Kumar - 1993
21 Parallel formulation of interior point algorithms - Karypis, Gupta et al. - 1994
18 Distributed solution of sparse linear systems - Heath, Raghavan - 1993
17 The fan-both family of column-based distributed cholesky fac.. (context) - Ashcraft - 1993
17 direct-connect communications technology (context) - Nugent - 1988
17 Limiting communication in parallel sparse Cholesky factoriza.. (context) - Hulbert, Zmijewski - 1991
16 Efficient parallel solutions of large sparse SPD systems on .. - Sun - 1992
16 SHAPE: A parallelization tool for sparse matrix computations (context) - Venugopal, Naik - 1992
15 Communication reduction in parallel sparse Cholesky factoriz.. (context) - George, Liu et al. - 1987
15 Distributed multifrontal factorization using clique trees (context) - Pothen, Sun - 1991
14 Effects of partitioning and scheduling sparse matrix factori.. (context) - Venugopal, Naik - 1991
10 A grid-based subtree-subcube assignment strategy for solving.. (context) - John, Rice - 1992
10 Assignment and scheduling in parallel matrix factorization (context) - O'Leary, Stewart - 1986
9 segment partition for the factorization of sparse symmetric .. (context) - Ashcraft - 1990
9 Solving planar systems of equations on distributed-memory mu.. (context) - Lucas - 1987
9 Computer Science Department (context) - Pothen, Simon et al. - 1992
8 Data traffic reduction schemes Cholesky factorization on ayn.. (context) - Naik, Patrick - 1989
7 Parallel algorithms for forward and back substitution in dir.. - Gupta, Kumar - 1995
7 Performance evaluation of the parallel multifrontal method i.. (context) - Pozo, Smith - 1993
7 Distributed sparse matrix factorization: QR and Cholesky fac.. (context) - Raghavan - 1991
6 Solutions Manual for Introduction to Parallel Computing (context) - Kumar, Grama et al. - 1994
5 Partioning sparce matrices with eigenvectors of graphs (context) - Pothen, Simon et al. - 1990
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