J. Demmel. Numerical Linear Algebra on Parallel Processors. Lecture Notes for NSF-CBMS Regional Conference in the Mathematical Sciences, June 1995. To be published as a book by SIAM. 95 Home/Search Document Not in Database Summary Related Articles Check |
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S+: Efficient 2D Sparse LU Factorization on Parallel Machines - Shen, Yang, Jiao (Correct)
....sequence associated with those columns and updating the lower triangular portion of column block k. The pivoting sequence is held until the factorization of the kth column block is completed. Then the pivoting sequence is applied to the rest of the matrix. This is called delayed pivoting [3]. Task Update(k; j) uses column block k (L k;k ; L k 1;k ; Delta Delta Delta ; LN;k ) to modify column block j. That includes row swapping which applies the pivoting derived by F actor(k) to column block j, scaling that uses the factorized submatrix L k;k to scale U k;j , and updating ....
J. Demmel, Numerical Linear Algebra on Parallel Processors. Lecture Notes for NSF-CBMS Regional Conference in the Mathematical Sciences, June 1995.
Efficient Sparse Gaussian Elimination with Lazy Space Allocation - Jiang (1999) (Correct)
....of graph scheduling techniques and efficient run time support to exploit irregular parallelism. We observe that on most current commodity processors with memory hierarchies, a highly optimized BLAS 3 subroutine usually outperforms a BLAS 2 subroutine in implementing the same numerical operations [6, 8]. We can afford to introduce some extra BLAS 3 operations in re designing the LU algorithm so that the new algorithm is easily parallelized but the sequential performance of this code is still competitive to the current best sequential code. We use the static symbolic factorization technique first ....
....sequence associated with those columns and updating the lower triangular portion of column block k. The pivoting sequence is held until the factorization of the k th column block is completed. Then the pivoting sequence is applied to the rest of the matrix. This is called delayed pivoting [6]. 2) Task Update(k; j) uses column block k (A k;k ; A k 1;k ; Delta Delta Delta ; AN;k ) to modify column block j. That includes row swapping using the result of pivoting derived by F actor(k) scaling which uses the fac 20 torized submatrix A k;k to scale A k;j , and updating which ....
J. Demmel. Numerical Linear Algebra on Parallel Processors. Lecture Notes for NSF-CBMS Regional Conference in the Mathematical Sciences, June 1995. 48
Elimination Forest Guided 2D Sparse LU Factorization - Shen, Jiao, Yang (1998) (2 citations) (Correct)
.... can be used, for which fast parallel algorithms have been developed [15, 19, 20] When pivoting is required to maintain numerical stability A short version of this paper will appear in the 10th annual ACM Symposium on Parallel Algorithms and Architectures for non symmetric linear systems [2, 14], it is very hard to produce high performance for this problem because partial pivoting operations dynamically change computation and communication patterns during the elimination process, and cause severe caching miss and load imbalance on modern computers with memory hierarchies. The previous ....
....sequence associated with those columns and updating the lower triangular portion of column block k. The pivoting sequence is held until the factorization of the k th column block is completed. Then the pivoting sequence is applied to the rest of the matrix. This is called delayed pivoting [2]. 2) Task Update(k; j) uses column block k (A k;k ; A k 1;k ; Delta Delta Delta ; AN;k ) to modify column block j. That includes row swapping using the result of pivoting derived by F actor(k) scaling which uses the factorized submatrix A k;k to scale A k;j , and updating which uses ....
J. Demmel. Numerical Linear Algebra on Parallel Processors. Lecture Notes for NSF-CBMS Regional Conference in the Mathematical Sciences, June 1995.
Parallel Sparse LU Factorization with Partial Pivoting on.. - Fu, Jiao, Yang (1997) (1 citation) (Correct)
.... can be used, for which fast sequential and parallel algorithms have been developed in [21, 26, 27] However in many applications, the associated equation systems involve nonsymmetric matrices and pivoting may be necessary to maintain numerical stability for such nonsymmetric linear systems [6, 20]. Because pivoting operations interchange rows based on the numerical values of matrix elements during the elimination process, it is impossible to predict the precise structures of L and U factors without actually performing the numerical factorization. The adaptive and irregular nature of sparse ....
....maximum irregular parallelism and reducing memory requirements for solving large problems. We observe that on most current commodity processors with memory hierarchies, a highly optimized BLAS 3 subroutine usually outperforms a BLAS 2 subroutine in implementing the same numerical operations [6, 8]. We can afford to introduce some extra BLAS 3 operations in re designing the LU algorithm so that the new algorithm is easy to be parallelized but the sequential performance of this code is still competitive to the current best sequential code. We use the static symbolic factorization technique ....
[Article contains additional citation context not shown here]
J. Demmel. Numerical Linear Algebra on Parallel Processors. Lecture Notes for NSF-CBMS Regional Conference in the Mathematical Sciences, June 1995. To be published as a book by SIAM.
Efficient Sparse LU Factorization with Lazy Space Allocation - Jiang, Richman, Shen, Yang (1999) (1 citation) (Correct)
....sequence associated with those columns and updating the lower triangular portion of column block k. The pivoting sequence is held until the factorization of the k th column block is completed. Then the pivoting sequence is applied to the rest of the matrix. This is called delayed pivoting [3]. 2) Task Update(k; j) uses column block k (A k;k ; A k 1;k ; Delta Delta Delta ; AN;k ) to modify column block j. That includes row swapping using the result of pivoting derived by F actor(k) scaling which uses the factorized submatrix A k;k to scale A k;j , and updating which uses ....
J. Demmel. Numerical Linear Algebra on Parallel Processors. Lecture Notes for NSF-CBMS Regional Conference in the Mathematical Sciences, June 1995.
Efficient Sparse LU Factorization with Partial Pivoting on.. - Fu, Yang (1998) (10 citations) (Correct)
....such as circuit simulation, computational fluid dynamics and structural mechanics, the associated equation systems involve nonsymmetric matrices. Pivoting must be conducted to maintain numerical stability for such nonsymmetric linear systems and a typical strategy is partial column pivoting [3, 15]. Because the pivoting operations interchange rows based on the numerical values of matrix elements during the elimination process, it is impossible to predict the precise structures of L and U factors without actually performing the numerical factorization. The adaptive and irregular nature of ....
....of graph scheduling techniques and efficient run time support to exploit irregular parallelism. We observe that on most current commodity processors with memory hierarchies, a highly optimized BLAS 3 subroutine usually outperforms a BLAS 2 subroutine in implementing the same numerical operations [3, 5]. We can afford to introduce some extra BLAS 3 operations in re designing the LU algorithm so that the new algorithm is easy to be parallelized but the sequential performance of this code is still competitive to the current best sequential code. We use the static symbolic factorization technique ....
[Article contains additional citation context not shown here]
J. Demmel. Numerical Linear Algebra on Parallel Processors. Lecture Notes for NSF-CBMS Regional Conference in the Mathematical Sciences, June 1995. To be published as a book by SIAM.
Sparse LU Factorization with Partial Pivoting on Distributed.. - Fu, Yang (1996) (1 citation) (Correct)
....such as circuit simulation, computational fluid dynamics and structural mechanics, the associated equation systems involve nonsymmetric matrices. Pivoting must be conducted to maintain numerical stability for such nonsymmetric linear systems and a typical strategy is partial column pivoting [3, 16]. Because the pivoting operations interchange rows based on the numerical values of matrix elements during the elimination process, it is impossible to predict the precise structures of L and U factors without actually performing the numerical factorization. The adaptive and irregular nature of ....
....of graph scheduling techniques and efficient run time support to exploit irregular parallelism. We observe that on most current commodity processors with memory hierarchies, a highly optimized BLAS 3 subroutine usually outperforms a BLAS 2 subroutine in implementing the same numerical operations [3, 5]. We can afford to introduce some extra BLAS 3 operations in re designing the LU algorithm so that the new algorithm is easy to be parallelized but the sequential performance of this code is still competitive to the current best sequential code. We use the static symbolic factorization technique ....
[Article contains additional citation context not shown here]
J. Demmel. Numerical Linear Algebra on Parallel Processors. Lecture Notes for NSF-CBMS Regional Conference in the Mathematical Sciences, June 1995. To be published as a book by SIAM.
Efficient Sparse LU Factorization with Partial Pivoting on.. - Fu, Jiao, Yang (1998) (10 citations) (Correct)
.... can be used, for which fast sequential and parallel algorithms have been developed in [24, 30, 31] However in many applications, the associated equation systems involve nonsymmetric matrices and pivoting may be required to maintain numerical stability for such nonsymmetric linear systems [6, 23]. Because Currently with the Computer Science Department, University of Illinois at Urbana Champaign. pivoting operations interchange rows based on the numerical values of matrix elements during the elimination process, it is impossible to predict the precise structures of L and U factors ....
....maximum irregular parallelism and reducing memory requirements for solving large problems. We observe that on most current commodity processors with memory hierarchies, a highly optimized BLAS 3 subroutine usually outperforms a BLAS 2 subroutine in implementing the same numerical operations [6, 9]. We can afford to introduce some extra BLAS 3 operations in re designing the LU algorithm so that the new algorithm is easy to be parallelized but the sequential performance of this code is still competitive to the current best sequential code. We use the static symbolic factorization technique ....
[Article contains additional citation context not shown here]
J. Demmel. Numerical Linear Algebra on Parallel Processors. Lecture Notes for NSF-CBMS Regional Conference in the Mathematical Sciences, June 1995. To be published as a book by SIAM.
A Comparison of 1-D and 2-D Data Mapping for Sparse LU.. - Fu, Jiao, Yang (Correct)
....finding the pivoting sequence associated with those columns and updating the lower triangular portion of panel k. The pivoting sequence is held until the factorization of the k th panel is completed. Then the pivoting sequence is applied to the rest of the matrix. This is called delayed pivoting [2]. The F actor( tasks mainly use BLAS 1 and BLAS 2 subroutines. 2) Task Update(k; j) is to use panel k to modify panel j. That includes row swapping using the result of pivoting derived by F actor(k) scaling which uses the factorized A k;k to scale A k;j , and updating which uses A i;k and ....
J. Demmel, Numerical Linear Algebra on Parallel Processors. Lecture Notes for NSF-CBMS Regional Conference in the Mathematical Sciences, June 1995.
Parallel Sparse Gaussian Elimination with Partial Pivoting and 2-D .. - Jiao (1997) (2 citations) (Correct)
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J. Demmel. Numerical Linear Algebra on Parallel Processors. Lecture Notes for NSF-CBMS Regional Conference in the Mathematical Sciences, June 1995. To be published as a book by SIAM. 95
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