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## Using postordering and static symbolic factorization for parallel sparse LU (2000)

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### Other Repositories/Bibliography

Venue: | In Proceedings of the International Parallel and Distributed Processing Symposium (IPDPS |

Citations: | 3 - 0 self |

### Citations

203 |
The role of elimination trees in sparse factorization,
- Liu
- 1990
(Show Context)
Citation Context ...e § element is the element � on row � and column ����� ofs. The number equals the number of elements in � the th row � ����� ofs. An important data structure is the elimination tree (etree for short) =-=[9]-=-; first introduced for the sparse Cholesky factorization, it has proven to be very useful in the symmetric case and it has later been adapted for the unsymmetric case. The SuperLU package employs the ... |

95 | An asynchronous parallel supernodal algorithm for sparse Gaussian elimination.
- Gilbert, Demmel, et al.
- 1999
(Show Context)
Citation Context ...ore parallelism can be exploited. Two approaches have been developed for the LU factorization of a sparse matrix: submatrix-based methods [1] and column-based (more recently supernodal-based) methods =-=[2]-=-. Our LU factorization research was based on two implementations of supernodal methods. The SuperLU [2] package is designed for an existing threading model on the shared memory machines. On the other ... |

72 |
On algorithms for obtaining a maximum transversal.
- DUFF
- 1981
(Show Context)
Citation Context ...r. Then, we can consider thatshas a zero-free diagonal (it’s always possible to permutes’s rows using a transversal thus transformings© § © ¦ § � � £¥¤ � � § � § � ’s diagonal to a zero-free diagonal =-=[3]-=-). A characterization of the rows of using the elimination tree for unsymmetric matrices was proposed in [7]. In that paper, every row is represented by a branch of the etree, branch that belongs to .... |

43 |
Symbolic factorization for sparse Gaussian elimination with partial pivoting
- George, Ng
- 1987
(Show Context)
Citation Context ...hich can later appear in the numerical factorization, due to pivoting (pivoting may be required if A unsymmetric; this structure can be determined by an efficient static symbolic factorization scheme =-=[6]-=-. This way, the LU factorization is computedson instead § ofs. Even if some operations will involve zero elements (S* [5], S+ [10]), recent developments show that some of the zero blocks can be elimin... |

33 | Efficient Sparse LU Factorization with Partial Pivoting on Distributed Memory Architectures
- Fu, Jiao, et al.
(Show Context)
Citation Context ...orization research was based on two implementations of supernodal methods. The SuperLU [2] package is designed for an existing threading model on the shared memory machines. On the other hand, the S* =-=[5]-=- and S+ [10] implementations are built for distributed memory machines, giving a better scalability. In order to present the contributions of this paper we first present the sequence of steps for a sp... |

29 | MUMPS MUltifrontal Massively Parallel Solver Version 2.0
- Amestoy, Duff, et al.
- 1998
(Show Context)
Citation Context ...ements are smaller, computation requirements are reduced and more parallelism can be exploited. Two approaches have been developed for the LU factorization of a sparse matrix: submatrix-based methods =-=[1]-=- and column-based (more recently supernodal-based) methods [2]. Our LU factorization research was based on two implementations of supernodal methods. The SuperLU [2] package is designed for an existin... |

20 |
Parallel sparse Gaussian elimination with partial pivoting
- George, Ng
- 1990
(Show Context)
Citation Context ...sversal thus transformings© § © ¦ § � � £¥¤ � � § � § � ’s diagonal to a zero-free diagonal [3]). A characterization of the rows of using the elimination tree for unsymmetric matrices was proposed in =-=[7]-=-. In that paper, every row is represented by a branch of the etree, branch that belongs to . A characterization of the columns of is not known in the surveyed literature. The next theorems will help d... |

13 |
An ecient parallel sparse partial pivoting algorithm
- Gilbert
- 1988
(Show Context)
Citation Context ...ng the Columns in independent subtrees of the elimination tree can be computed without referring to any common elements, because the source columns in the updates have completely disjoint row indices =-=[8]-=-. � ��� Let be nodes £ ��§ � of , neither of which is an an��� cestor of the � other, and another node such that � the � tasks � � � � ��� � � � exist. Then there is no dependence be� ��� tween the tw... |

12 | Elimination forest guided 2D sparse LU factorization
- Shen, Jiao, et al.
- 1998
(Show Context)
Citation Context ...esearch was based on two implementations of supernodal methods. The SuperLU [2] package is designed for an existing threading model on the shared memory machines. On the other hand, the S* [5] and S+ =-=[10]-=- implementations are built for distributed memory machines, giving a better scalability. In order to present the contributions of this paper we first present the sequence of steps for a sparse LU fact... |

1 |
Scheduling and Runtime Support for Irregular Computations
- Fu
- 1997
(Show Context)
Citation Context ...wn in figure 4(c). In figure 4(b) we show the dependence graph for the same matrix which was used in the S* package. In order to schedule the LU task dependence graph we used the RAPID runtime system =-=[4]-=-. It creates a schedule in two steps: first, it analyzes data accesses for each task, thus obtaining a task dependence graph and second it efficiently distributes these tasks on a distributed memory m... |