A column approximate minimum degree ordering algorithm

Journal Article · Wed Nov 01 04:00:00 EST 2000 · SIAM Journal on Matrix Analysis & Applications

OSTI ID:834481

Davis, Timothy A ^[1]; Gilbert, John R; Larimore, Stefan I; Ng, Esmond G

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1. LBNL Library

Sparse Gaussian elimination with partial pivoting computes the factorization PAQ = LU of a sparse matrix A, where the row ordering P is selected during factorization using standard partial pivoting with row interchanges. The goal is to select a column preordering, Q, based solely on the nonzero pattern of A such that the factorization remains as sparse as possible, regardless of the subsequent choice of P. The choice of Q can have a dramatic impact on the number of nonzeros in L and U. One scheme for determining a good column ordering for A is to compute a symmetric ordering that reduces fill-in in the Cholesky factorization of A'A. This approach, which requires the sparsity structure of A'A to be computed, can be expensive both in terms of space and time since A'A may be much denser than A. An alternative is to compute Q directly from the sparsity structure of A; this strategy is used by Matlab's COLAMD preordering algorithm. A new ordering algorithm, COLAMD, is presented. It is based on the same strategy but uses a better ordering heuristic. COLAMD is faster and computes better orderings, with fewer nonzeros in the factors of the matrix.

• Research Organization: Ernest Orlando Lawrence Berkeley National Laboratory, Berkeley, CA (US)
• Sponsoring Organization: USDOE Director, Office of Science. Office of Advanced Scientific Computing Research. Mathematical, Information, and Computational Sciences Division; National Science Foundation (US)
• DOE Contract Number: AC03-76SF00098
• OSTI ID: 834481
• Report Number(s): LBNL--47109; TR-00-005
• Journal Information: SIAM Journal on Matrix Analysis & Applications, Journal Name: SIAM Journal on Matrix Analysis & Applications Journal Issue: 4 Vol. 17
• Country of Publication: United States
• Language: English

Related Subjects

99 GENERAL AND MISCELLANEOUS
ALGORITHMS
FACTORIZATION
LAWRENCE BERKELEY LABORATORY
SPARSE NONSYMMETRIC MATRICES LINEAR EQUATIONS ORDERING METHODS