## Finding Good Column Orderings for Sparse QR Factorization (1996)

Venue: | In Second SIAM Conference on Sparse Matrices |

Citations: | 17 - 0 self |

### BibTeX

@TECHREPORT{Heggernes96findinggood,

author = {Pinar Heggernes and Pontus Matstoms},

title = {Finding Good Column Orderings for Sparse QR Factorization},

institution = {In Second SIAM Conference on Sparse Matrices},

year = {1996}

}

### Years of Citing Articles

### OpenURL

### Abstract

For sparse QR factorization, finding a good column ordering of the matrix to be factorized, is essential. Both the amount of fill in the resulting factors, and the number of floating-point operations required by the factorization, are highly dependent on this ordering. A suitable column ordering of the matrix A is usually obtained by minimum degree analysis on A T A. The objective of this analysis is to produce low fill in the resulting triangular factor R. We observe that the efficiency of sparse QR factorization is also dependent on other criteria, like the size and the structure of intermediate fill, and the size and the structure of the frontal matrices for the multifrontal method, in addition to the amount of fill in R. An important part of this information is lost when A T A is formed. However, the structural information from A is important to consider in order to find good column orderings. We show how a suitable equivalent reordering of an initial fill-reducing ordering can...