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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... (Update)
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...ordering of A are the minimum degree algorithm and nested dissection. We will not address this problem further here but refer to [1, 9, 14, 22]. Since P r A = P r Q 1 )R the row ordering of A will not affect the number of nonzeros in Q 1 , only their locations. However, as...
...factorization of the original matrix A, regardless of how P is chosen. Another application of column orderings is sparse QR factorization [33]. In order to control the ll in that occurs when A is sparse, we need to know the nonzero patterns of the matrices A (k) for each k...
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BibTeX entry: (Update)
P. Heggernes and P. Matstoms. Finding good column orderings for sparse QR factorization. Technical Report LiTH-MAT-R-1996-20, Departement of Mathematics, Linkopings University, 1996. http://citeseer.ist.psu.edu/heggernes96finding.html More
@techreport{ heggernes96finding,
author = "P. Heggernes and P. Matstoms",
title = "Finding good column orderings for sparse {QR} factorization",
number = "LiTH-MAT-R-1996-20",
institution = "Departement of Mathematics, Linkopings University",
year = "1996",
url = "citeseer.ist.psu.edu/heggernes96finding.html" }
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