### Predicting fill for sparse orthogonal factorizationPredicting fill for sparse orthogonal factorization

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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