NDLI: Matrix Sparsification for Rank and Determinant Computations via Nested Dissection

Content Provider	IEEE Xplore Digital Library
Author	Yuster, R.
Copyright Year	2008
Description	Author affiliation: Univ. of Haifa, Haifa (Yuster, R.)
Abstract	The nested dissection method developed by Lipton, Rose, and Tarjan is a seminal method for quickly performing Gaussian elimination of symmetric real positive definite matrices whose support structure satisfies good separation properties (e.g. planar). One can use the resulting LU factorization to deduce various parameters of the matrix. The main results of this paper show that we can remove the three restrictions of being "symmetric", being "real", and being "positive definite" and still be able to compute the rank and, when relevant, also the absolute determinant, while keeping the running time of nested dissection. Our results are based, in part, on an algorithm that, given an arbitrary square matrix A of order n having m non-zero entries, creates another square matrix B of order n + 2t = O(m) with the property that each row and each column of B contains at most three nonzero entries, and, furthermore, rank(B) = rank (A) + 2t and det(B) = det(A). The running time of this algorithm is only O(m), which is optimal.
Starting Page	137
Ending Page	145
File Size	295356
Page Count	9
File Format	PDF
ISBN	9780769534367
ISSN	02725428
DOI	10.1109/FOCS.2008.14
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2008-10-25
Publisher Place	USA
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Transmission line matrix methods Symmetric matrices Sparse matrices Particle separators Tree graphs Computer science NP-hard problem Monte Carlo methods Arithmetic nested-dissection matrix rank determinant
Content Type	Text
Resource Type	Article

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