The Experts below are selected from a list of 39 Experts worldwide ranked by ideXlab platform
K Parthasarathy - One of the best experts on this subject based on the ideXlab platform.
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variable Pivot Column oriented givens rotations based power system state estimator
International Journal of Electrical Power & Energy Systems, 1998Co-Authors: A Pandian, S A Soman, K ParthasarathyAbstract:The numerically stable power system state estimation (PSSE) algorithm uses a Givens rotations based least square (LS) solver. Row and Column ordering techniques are used to reduce computations as well fills arising during sparse matrix QR decomposition. Row oriented algorithm is popularly used for QR decomposition in PSSE application with a priori row and Column ordering to reduce fills. This paper proposes online variable Pivot row and Column ordering techniques for sparse QR decomposition, which locally reduce fills during each rotation operation. Use of online ordering techniques requires a shift from row oriented QR decomposition to Column oriented QR decomposition. Simulation results on large power systems demonstrate the benefits of the proposed approach in comparison to row oriented QR decomposition.
Jennifer A. Scott - One of the best experts on this subject based on the ideXlab platform.
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Compressed Threshold Pivoting for Sparse Symmetric Indefinite Systems
SIAM Journal on Matrix Analysis and Applications, 2014Co-Authors: Jd Hogg, Jennifer A. ScottAbstract:A key technique for controlling numerical stability in sparse direct solvers is threshold partial Pivoting. When selecting a Pivot, the entire candidate Pivot Column below the diagonal must be up-to-date and must be scanned. If the factorization is parallelized across a large number of cores, communication latencies can be the dominant computational cost. In this paper, we propose two alternative Pivoting strategies for sparse symmetric indefinite matrices of full rank that significantly reduce communication by compressing the necessary data into a small matrix that can be used to select Pivots. Once Pivots have been chosen, they can be applied in a communication-efficient fashion. For an $n\times p$ submatrix on $P$ processors, we show our methods perform a factorization using $O(\log P)$ messages instead of the $O(p\log P)$ for threshold partial Pivoting. The additional costs in terms of operations and communication bandwidth are relatively small. A stability proof is given and numerical results using a...
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Compressed threshold Pivoting for sparse symmetric indefinite systems
arXiv: Numerical Analysis, 2013Co-Authors: Jd Hogg, Jennifer A. ScottAbstract:A key technique for controlling numerical stability in sparse direct solvers is threshold partial Pivoting. When selecting a Pivot, the entire candidate Pivot Column below the diagonal must be up-to-date and must be scanned. If the factorization is parallelized across a large number of cores, communication latencies can be the dominant computational cost. In this paper, we propose two alternative Pivoting strategies for sparse symmetric indefinite matrices that significantly reduce communication by compressing the necessary data into a small matrix that can be used to select Pivots. Once Pivots have been chosen, they can be applied in a communication-efficient fashion. For an n x p submatrix on P processors, we show our methods perform a factorization using O(log P) messages instead of the O(p log P) for threshold partial Pivoting. The additional costs in terms of operations and communication bandwidth are relatively small. A stability proof is given and numerical results using a range of symmetric indefinite matrices arising from practical problems are used to demonstrate the practical robustness. Timing results on large random examples illustrate the potential speedup on current multicore machines.
A Pandian - One of the best experts on this subject based on the ideXlab platform.
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variable Pivot Column oriented givens rotations based power system state estimator
International Journal of Electrical Power & Energy Systems, 1998Co-Authors: A Pandian, S A Soman, K ParthasarathyAbstract:The numerically stable power system state estimation (PSSE) algorithm uses a Givens rotations based least square (LS) solver. Row and Column ordering techniques are used to reduce computations as well fills arising during sparse matrix QR decomposition. Row oriented algorithm is popularly used for QR decomposition in PSSE application with a priori row and Column ordering to reduce fills. This paper proposes online variable Pivot row and Column ordering techniques for sparse QR decomposition, which locally reduce fills during each rotation operation. Use of online ordering techniques requires a shift from row oriented QR decomposition to Column oriented QR decomposition. Simulation results on large power systems demonstrate the benefits of the proposed approach in comparison to row oriented QR decomposition.
Jd Hogg - One of the best experts on this subject based on the ideXlab platform.
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Compressed Threshold Pivoting for Sparse Symmetric Indefinite Systems
SIAM Journal on Matrix Analysis and Applications, 2014Co-Authors: Jd Hogg, Jennifer A. ScottAbstract:A key technique for controlling numerical stability in sparse direct solvers is threshold partial Pivoting. When selecting a Pivot, the entire candidate Pivot Column below the diagonal must be up-to-date and must be scanned. If the factorization is parallelized across a large number of cores, communication latencies can be the dominant computational cost. In this paper, we propose two alternative Pivoting strategies for sparse symmetric indefinite matrices of full rank that significantly reduce communication by compressing the necessary data into a small matrix that can be used to select Pivots. Once Pivots have been chosen, they can be applied in a communication-efficient fashion. For an $n\times p$ submatrix on $P$ processors, we show our methods perform a factorization using $O(\log P)$ messages instead of the $O(p\log P)$ for threshold partial Pivoting. The additional costs in terms of operations and communication bandwidth are relatively small. A stability proof is given and numerical results using a...
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Compressed threshold Pivoting for sparse symmetric indefinite systems
arXiv: Numerical Analysis, 2013Co-Authors: Jd Hogg, Jennifer A. ScottAbstract:A key technique for controlling numerical stability in sparse direct solvers is threshold partial Pivoting. When selecting a Pivot, the entire candidate Pivot Column below the diagonal must be up-to-date and must be scanned. If the factorization is parallelized across a large number of cores, communication latencies can be the dominant computational cost. In this paper, we propose two alternative Pivoting strategies for sparse symmetric indefinite matrices that significantly reduce communication by compressing the necessary data into a small matrix that can be used to select Pivots. Once Pivots have been chosen, they can be applied in a communication-efficient fashion. For an n x p submatrix on P processors, we show our methods perform a factorization using O(log P) messages instead of the O(p log P) for threshold partial Pivoting. The additional costs in terms of operations and communication bandwidth are relatively small. A stability proof is given and numerical results using a range of symmetric indefinite matrices arising from practical problems are used to demonstrate the practical robustness. Timing results on large random examples illustrate the potential speedup on current multicore machines.
S A Soman - One of the best experts on this subject based on the ideXlab platform.
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variable Pivot Column oriented givens rotations based power system state estimator
International Journal of Electrical Power & Energy Systems, 1998Co-Authors: A Pandian, S A Soman, K ParthasarathyAbstract:The numerically stable power system state estimation (PSSE) algorithm uses a Givens rotations based least square (LS) solver. Row and Column ordering techniques are used to reduce computations as well fills arising during sparse matrix QR decomposition. Row oriented algorithm is popularly used for QR decomposition in PSSE application with a priori row and Column ordering to reduce fills. This paper proposes online variable Pivot row and Column ordering techniques for sparse QR decomposition, which locally reduce fills during each rotation operation. Use of online ordering techniques requires a shift from row oriented QR decomposition to Column oriented QR decomposition. Simulation results on large power systems demonstrate the benefits of the proposed approach in comparison to row oriented QR decomposition.