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Making Sparse Gaussian Elimination Scalable by Static Pivoting
 In Proceedings of Supercomputing
, 1998
"... We propose several techniques as alternatives to partial pivoting to stabilize sparse Gaussian elimination. From numerical experiments we demonstrate that for a wide range of problems the new method is as stable as partial pivoting. The main advantage of the new method over partial pivoting is th ..."
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Cited by 44 (6 self)
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We propose several techniques as alternatives to partial pivoting to stabilize sparse Gaussian elimination. From numerical experiments we demonstrate that for a wide range of problems the new method is as stable as partial pivoting. The main advantage of the new method over partial pivoting
On The Complexity Of Sparse Gaussian Elimination Via Bordering
, 1990
"... . The complexity of a general sparse Gaussian elimination algorithm based on the bordering algorithm is analyzed. It has been shown that this procedure requires less integer overhead storage than more traditional general sparse procedures, but the complexity of the nonnumerical overhead calculations ..."
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. The complexity of a general sparse Gaussian elimination algorithm based on the bordering algorithm is analyzed. It has been shown that this procedure requires less integer overhead storage than more traditional general sparse procedures, but the complexity of the nonnumerical overhead
Sparse Gaussian Elimination on High Performance Computers
, 1996
"... Sparse Gaussian Elimination on High Performance Computers by XiaoyeS.Li Doctor of Philosophy in Computer Science University of California at Berkeley James W. Demmel, Chair This dissertation presents new techniques for solving large sparse unsymmetric linear systems on high performance compute ..."
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Sparse Gaussian Elimination on High Performance Computers by XiaoyeS.Li Doctor of Philosophy in Computer Science University of California at Berkeley James W. Demmel, Chair This dissertation presents new techniques for solving large sparse unsymmetric linear systems on high performance
Efficient Sparse Gaussian Elimination with Lazy Space Allocation
, 1999
"... A parallel algorithm is implemented for sparse Gaussian elimination on distributed memory machines. At First, we utilize the minimum degree ordering algorithm and transversal algorithm to reorder the columns and rows of the matrix. Next, we implement the LU factorization of the reordered matrix by ..."
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A parallel algorithm is implemented for sparse Gaussian elimination on distributed memory machines. At First, we utilize the minimum degree ordering algorithm and transversal algorithm to reorder the columns and rows of the matrix. Next, we implement the LU factorization of the reordered matrix
An asynchronous parallel supernodal algorithm for sparse Gaussian elimination
 SIAM Journal on Matrix Analysis and Applications
, 1999
"... Abstract. Although Gaussian elimination with partial pivoting is a robust algorithm to solve unsymmetric sparse linear systems of equations, it is difficult to implement efficiently on parallel machines because of its dynamic and somewhat unpredictable way of generating work and intermediate results ..."
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Cited by 95 (17 self)
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Abstract. Although Gaussian elimination with partial pivoting is a robust algorithm to solve unsymmetric sparse linear systems of equations, it is difficult to implement efficiently on parallel machines because of its dynamic and somewhat unpredictable way of generating work and intermediate
Sparse Gaussian Elimination on High Performance Computers
, 1996
"... This dissertation presents new techniques for solving large sparse unsymmetric linear systems on high performance computers, using Gaussian elimination with partial pivoting. The efficiencies of the new algorithms are demonstrated for matrices from various fields and for a variety of high performan ..."
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Cited by 40 (7 self)
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This dissertation presents new techniques for solving large sparse unsymmetric linear systems on high performance computers, using Gaussian elimination with partial pivoting. The efficiencies of the new algorithms are demonstrated for matrices from various fields and for a variety of high
Distributed Sparse Gaussian Elimination And Orthogonal Factorization
 LAPACK WORKING NOTE 64 (UT CS93203)
, 1993
"... We consider the solution of a linear system Ax = b on a distributed memory machine when the matrix A has full rank and is large, sparse and nonsymmetric. We use our Cartesian nested dissection algorithm to compute a fillreducing column ordering of the matrix. We develop algorithms that use the asso ..."
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Cited by 8 (3 self)
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the associated separator tree to estimate the structure of the factor and to distribute and perform numeric computations. When the matrix is nonsymmetric but square, the numeric computations involve Gaussian elimination with row pivoting; when the matrix is overdetermined, roworiented Householder transforms
Symbolic and Exact Structure Prediction for Sparse Gaussian Elimination with
 Partial Pivoting, in "SIAM Journal on Matrix Analysis and its Applications
"... Abstract. In this paper we consider two structure prediction problems of interest in Gaussian elimination with partial pivoting of sparse matrices. First, we consider the problem of determining the nonzero structure of the factors L and U during the factorization. We present an exact prediction of t ..."
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Cited by 1 (0 self)
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Abstract. In this paper we consider two structure prediction problems of interest in Gaussian elimination with partial pivoting of sparse matrices. First, we consider the problem of determining the nonzero structure of the factors L and U during the factorization. We present an exact prediction
An Asynchronous Parallel Supernodal Algorithm for Sparse Gaussian Elimination
 SIAM Journal on Matrix Analysis and Applications
, 1997
"... Although Gaussian elimination with partial pivoting is a robust algorithm to solve unsymmetric sparse linear systems of equations, it is difficult to implement efficiently on parallel machines, because of its dynamic and somewhat unpredictable way of generating work and intermediate results at ru ..."
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Although Gaussian elimination with partial pivoting is a robust algorithm to solve unsymmetric sparse linear systems of equations, it is difficult to implement efficiently on parallel machines, because of its dynamic and somewhat unpredictable way of generating work and intermediate results
Parallel Sparse Gaussian Elimination with Partial Pivoting and 2D Data Mapping
, 1997
"... Sparse Gaussian elimination with partial pivoting is a fundamental algorithm for many scientific and engineering applications, but it is still an open problem to develop a time and space efficient algorithm on distributed memory machines. In this thesis, we present an asynchronous algorithm which ..."
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Cited by 4 (2 self)
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Sparse Gaussian elimination with partial pivoting is a fundamental algorithm for many scientific and engineering applications, but it is still an open problem to develop a time and space efficient algorithm on distributed memory machines. In this thesis, we present an asynchronous algorithm which
Results 1  10
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