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Abstract: Given a sparse symmetric positive definite matrix AA and an associated sparse Cholesky factorization LDL , we develop sparse techniques for updating the factorization after either adding a collection of columns to A or deleting a collection of columns from A. Our techniques are based on an analysis and manipulation of the underlying graph structure, using the framework developed in an earlier paper on rank-1 modifications [T. A. Davis and W. W. Hager, SIAM J. Matrix Anal. Appl., 20... (Update)
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.... Cholesky factors of a sparse matrix after these small rank changes can be computed efficiently using the techniques developed in [3, 4]. In [8] we apply the DASA to quadratic network optimization, and compare it to other approaches. For linear programming, the strict...
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BibTeX entry: (Update)
T.A. Davis and W.W. Hager, "Multiple rank modifications of a sparse Cholesky factorization," SIAM Journal on Matrix Analysis and Applications, vol. 22, pp. 997--1013, 2001. http://citeseer.ist.psu.edu/davis01multiplerank.html More
@article{ davis01multiplerank,
author = "Timothy A. Davis and William W. Hager",
title = "Multiple-Rank Modifications of a Sparse {Cholesky} Factorization",
journal = "SIAM Journal on Matrix Analysis and Applications",
volume = "22",
number = "4",
pages = "997--1013",
year = "2001",
url = "citeseer.ist.psu.edu/davis01multiplerank.html" }
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