## A column approximate minimum degree ordering algorithm (2000)

Citations: | 253 - 50 self |

### BibTeX

@MISC{Davis00acolumn,

author = {Timothy A. Davis and et al.},

title = {A column approximate minimum degree ordering algorithm },

year = {2000}

}

### Years of Citing Articles

### OpenURL

### 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