TY - GEN
T1 - Nested-dissection orderings for sparse LU with partial pivoting
AU - Brainman, Igor
AU - Toledo, Sivan
N1 - Publisher Copyright:
© Springer-Verlag Berlin Heidelberg 2001.
PY - 2001
Y1 - 2001
N2 - We describe the implementation and performance of a novel fill-minimization ordering technique for sparse LU factorization with partial pivoting. The technique was proposed by Gilbert and Schreiber in 1980 but never implemented and tested. Like other techniques for ordering sparse matrices for LU with partial pivoting, our new method preorders the columns of the matrix (the row permutation is chosen by the pivoting sequence during the numerical factorization). Also like other methods, the column permutation Q that we select is a permutation that minimizes the fill in the Cholesky factor of QTATAQ. Unlike existing column-ordering techniques, which all rely on minimum-degree heuristics, our new method is based on a nested-dissection ordering of ATA. Our algorithm, however, never computes a representation of ATA, which can be expensive. We only work with a representation of A itself. Our experiments demonstrate that the method is efficient and that it can reduce fill significanly relative to the best existing methods. The method reduces the LU running time on some very large matrices (tens of millions of nonzeros in the factors) by more than a factor of 2.
AB - We describe the implementation and performance of a novel fill-minimization ordering technique for sparse LU factorization with partial pivoting. The technique was proposed by Gilbert and Schreiber in 1980 but never implemented and tested. Like other techniques for ordering sparse matrices for LU with partial pivoting, our new method preorders the columns of the matrix (the row permutation is chosen by the pivoting sequence during the numerical factorization). Also like other methods, the column permutation Q that we select is a permutation that minimizes the fill in the Cholesky factor of QTATAQ. Unlike existing column-ordering techniques, which all rely on minimum-degree heuristics, our new method is based on a nested-dissection ordering of ATA. Our algorithm, however, never computes a representation of ATA, which can be expensive. We only work with a representation of A itself. Our experiments demonstrate that the method is efficient and that it can reduce fill significanly relative to the best existing methods. The method reduces the LU running time on some very large matrices (tens of millions of nonzeros in the factors) by more than a factor of 2.
UR - http://www.scopus.com/inward/record.url?scp=0010969914&partnerID=8YFLogxK
U2 - 10.1007/3-540-45262-1_16
DO - 10.1007/3-540-45262-1_16
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AN - SCOPUS:0010969914
SN - 9783540418146
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 125
EP - 133
BT - Numerical Analysis and Its Applications - 2nd International Conference, NAA 2000, Revised Papers
A2 - Vulkov, Lubin
A2 - Yalamov, Plamen
A2 - Waniewski, Jerzy
PB - Springer Verlag
T2 - 2nd International Conference on Numerical Analysis and Its Applications, NAA 2000
Y2 - 11 June 2000 through 15 June 2000
ER -