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Author Coleman, Thomas F. ♦ Edenbrandt, Anders ♦ Gilbert, John R.
Source ACM Digital Library
Content type Text
Publisher Association for Computing Machinery (ACM)
File Format PDF
Copyright Year ©1986
Language English
Subject Domain (in DDC) Computer science, information & general works ♦ Data processing & computer science
Abstract In solving large sparse linear least squares problems $\textit{A}$ x ≃ b, several different numeric methods involve computing the same upper triangular factor $\textit{R}$ of $\textit{A}.$ It is of interest to be able to compute the nonzero structure of $\textit{R},$ given only the structure of $\textit{A}.$ The solution to this problem comes from the theory of matchings in bipartite graphs. The structure of $\textit{A}$ is modeled with a bipartite graph, and it is shown how the rows and columns of $\textit{A}$ 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 unnecessary space is needed for intermediate fill.
ISSN 00045411
Age Range 18 to 22 years ♦ above 22 year
Educational Use Research
Education Level UG and PG
Learning Resource Type Article
Publisher Date 1986-05-01
Publisher Place New York
e-ISSN 1557735X
Journal Journal of the ACM (JACM)
Volume Number 33
Issue Number 3
Page Count 16
Starting Page 517
Ending Page 532


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Source: ACM Digital Library