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Predicting Fill for Sparse Orthogonal Factorization

Author
Coleman, Thomas F.; Edenbrandt, Anders; Gilbert, John R.
Abstract
In solving large sparse linear least squares problems $Ax \cong b$, several different numeric methods involve computing the same upper triangular factor $R$ of $A$. It is of interest to be able to compute the nonzero structure of $R$, given only the structure of $A$. The solution to this problem comes from the theory of matchings in bipartite graphs. The structure of $A$ is modeled with a bipartite graph and it is shown how the rows and columns of $A$ can be rearranged into a structure from which the structure of its upper triangular factor can be correctly computed. Also, a new method for solving sparse least squares problems, called block back-substitution, is presented. This method assures that no unnecessary space is allocated for fill, and that no space is needed for intermediate fill.
Date Issued
1983-10Publisher
Cornell University
Subject
computer science; technical report
Previously Published As
http://techreports.library.cornell.edu:8081/Dienst/UI/1.0/Display/cul.cs/TR83-578
Type
technical report