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Highly Parallel Sparse Triangular Solution
, 1992
"... In this paper we survey a recent approach for solving sparse triangular systems of equations on highly parallel computers. This approach employs a partitioned representation of the inverse of the triangular matrix so that the solution can be computed by matrixvector multiplication. The number of fa ..."
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Cited by 27 (4 self)
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In this paper we survey a recent approach for solving sparse triangular systems of equations on highly parallel computers. This approach employs a partitioned representation of the inverse of the triangular matrix so that the solution can be computed by matrixvector multiplication. The number
Performance Of Parallel Sparse Triangular Solution
, 1998
"... Many applications require the solution of a sequence of sparse linear systems with the same matrix but different righthandside vectors. When the matrix is very large and sparse, the sparse matrix factors are computed in parallel and used in forward and back substitution steps to compute the soluti ..."
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Cited by 7 (5 self)
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Many applications require the solution of a sequence of sparse linear systems with the same matrix but different righthandside vectors. When the matrix is very large and sparse, the sparse matrix factors are computed in parallel and used in forward and back substitution steps to compute
Triangular Solution of Linear Systems in Tensor Product Format
"... This paper presents an algorithm to solve linear systems expressed by a matrix stored in a tensor product format. The proposed solution is based on a LU decomposition of the matrix keeping the tensor product structure. It is shown that the complexity of the decomposition is negligible and the backwa ..."
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Cited by 2 (0 self)
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This paper presents an algorithm to solve linear systems expressed by a matrix stored in a tensor product format. The proposed solution is based on a LU decomposition of the matrix keeping the tensor product structure. It is shown that the complexity of the decomposition is negligible
Evaluation of Sparse LU Factorization and Triangular Solution on Multicore Platforms ⋆
"... Abstract. The Chip Multiprocessor (CMP) will be the basic building block for computer systems ranging from laptops to supercomputers. New software developments at all levels are needed to fully utilize these systems. In this work, we evaluate performance of different highperformance sparse LU factor ..."
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Cited by 2 (0 self)
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factorization and triangular solution algorithms on several representative multicore machines. We include both pthreads and MPI implementations in this study, and found that the pthreads implementation consistently delivers good performance and a leftlooking algorithm is usually superior. 1
Parallel Sparse Triangular Solution with Partitioned Inverses and Prescheduled DAGs
, 1995
"... Sparse triangular solution offers a challenging irregular problem for parallel systems. The repeated solution of the system Lx = b, where L is a lower triangular factor of a sparse matrix, arises in numerous applications. A previous study [1] has shown that, if L is an incomplete factor, Lx = b can ..."
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Cited by 8 (4 self)
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Sparse triangular solution offers a challenging irregular problem for parallel systems. The repeated solution of the system Lx = b, where L is a lower triangular factor of a sparse matrix, arises in numerous applications. A previous study [1] has shown that, if L is an incomplete factor, Lx = b can
Partitioning A Chordal Graph Into Transitive Subgraphs For Parallel Sparse Triangular Solution
, 1992
"... . A recent approach for solving sparse triangular systems of equations on massively parallel computers employs a factorization of the triangular coefficient matrix to obtain a representation of its inverse in product form. The number of general communication steps required by this approach is propor ..."
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Cited by 14 (4 self)
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. A recent approach for solving sparse triangular systems of equations on massively parallel computers employs a factorization of the triangular coefficient matrix to obtain a representation of its inverse in product form. The number of general communication steps required by this approach
A New DataMapping Scheme For LatencyTolerant Distributed Sparse Triangular Solution
 In SuperComputing 2002 (2002
, 2002
"... This paper concerns latencytolerant schemes for the e#cient parallel solution of sparse triangular linear systems on distributed memory multiprocessors. Such triangular solution is required when sparse Cholesky factors are used to solve for a sequence of righthandside vectors or when incomplete s ..."
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Cited by 5 (2 self)
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This paper concerns latencytolerant schemes for the e#cient parallel solution of sparse triangular linear systems on distributed memory multiprocessors. Such triangular solution is required when sparse Cholesky factors are used to solve for a sequence of righthandside vectors or when incomplete
The accuracy of solutions to triangular systems
 SIAM J. Numer. Anal
, 1989
"... Abstract. Triangular systems play a fundamental role in matrix computations. It has been prominently stated in the literature, but is perhaps not widely appreciated, that solutions to triangular systems are usually computed to high accuracyhigher than the traditional condition numbers for linear s ..."
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Cited by 14 (6 self)
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Abstract. Triangular systems play a fundamental role in matrix computations. It has been prominently stated in the literature, but is perhaps not widely appreciated, that solutions to triangular systems are usually computed to high accuracyhigher than the traditional condition numbers for linear
Results 1  10
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1,349