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Abstract: A well known approach to compute the LU factorization of a general unsymmetric matrix A is to build the elimination tree associated with the pattern of the symmetric matrix A+A T and use it as a computational graph to drive the numerical factorization. This approach, although very efficient on a large range of unsymmetric matrices, does not capture the unsymmetric structure of the matrices. We introduce a new algorithm which detects and exploits the structural asymmetry of the submatrices... (Update)
Context of citations to this paper: More
.... description of the algorithms, the reader should consult previous papers by the authors of these algorithms (Amestoy et al. 1999, Amestoy et al. 2000, Li and Demmel 1998, Li and Demmel 1999) Both algorithms can be described by a computational tree whose nodes represent...
...Level 3 BLAS to perform the elimination operations. However, in MUMPS the frontal matrices are always square. It is shown in Amestoy and Puglisi (2000) how one can detect and exploit sparsity within the frontal matrices but the present implementation takes no advantage of...
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BibTeX entry: (Update)
Amestoy, P. R. and Puglisi, C. (2000), An unsymmetrized multifrontal LU factorization, Technical Report RT/APO/00/3, ENSEEIHT-IRIT. Also Lawrence Berkeley National Laboratory Report LBNL-46474. http://citeseer.ist.psu.edu/article/amestoy00unsymmetrized.html More
@misc{ amestoy00unsymmetrized,
author = "P. Amestoy and C. Puglisi",
title = "An unsymmetrized multifrontal LU factorization",
text = "Amestoy, P. R. and Puglisi, C. (2000), An unsymmetrized multifrontal LU
factorization, Technical Report RT/APO/00/3, ENSEEIHT-IRIT. Also Lawrence
Berkeley National Laboratory Report LBNL-46474.",
year = "2000",
url = "citeseer.ist.psu.edu/article/amestoy00unsymmetrized.html" }
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98 An approximate minimum degree ordering algorithm - Amestoy, Davis et al. - 1996
63 An unsymmetric-pattern multifrontal method for sparse LU fac.. - Davis, Du - 1997
57 The multifrontal solution of unsymmetric sets of linear syst.. (context) - Du, Reid - 1984
57 The multifrontal method for sparse matrix solution: Theory a.. (context) - Liu - 1992
56 Vectorization of a multiprocessor multifrontal code (context) - Amestoy, Du - 1989
40 Multifrontal parallel distributed symmetric and unsymmetric .. - Amestoy, Du et al. - 2000
34 Elimination structures for unsymmetric sparse lu factors - Gilbert, Liu - 1993
32 A fully asynchronous multifrontal solver using distributed d.. - Amestoy, Du et al. - 1999
30 A new implementation of sparse Gaussian elimination (context) - Schreiber - 1982
25 Memory management issues in sparse multifrontal methods on m.. (context) - Amestoy, Du - 1993
23 On algorithms for permuting large entries to the diagonal of.. - Du, Koster - 1999
23 multifrontal method for unsymmetric sparse matrices (context) - Davis, Du et al. - 1999
23 The Rutherford-Boeing Sparse Matrix Collection (context) - Du, Grimes et al. - 1997
20 The multifrontal solution of indenite sparse symmetric linea.. (context) - Du, Reid - 1983
17 Exploiting structural symmetry in unsymmetric sparse symboli.. (context) - Eisenstat, Liu - 1992
15 A scalable sparse direct solver using static pivoting - Li, Demmel - 1999
4 a set of Fortran subroutines for solving sparse symmetric se.. (context) - Du, Reid - 1982
3 Stable nite elements for problems with wild constraints (context) - Vavasis - 1996
3 Full matrix techniques in sparse Gaussian elimination (context) - Du - 1981
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