A column approximate minimum degree ordering algorithm (2000)
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BibTeX
@MISC{Davis00acolumn,
author = {Timothy A. Davis and et al.},
title = {A column approximate minimum degree ordering algorithm },
year = {2000}
}
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Abstract
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 ATA. This approach, which requires the sparsity structure of ATA to be computed, can be expensive both in
