NDLI: Heuristic Spectral Techniques for the Reduction of Bandwidth and Work-Bound of Sparse Matrices

Content Provider	Springer Nature Link
Author	Del Corso, Gianna M. Romani, Francesco
Copyright Year	2001
Abstract	In this paper, we present heuristic techniques for the reduction of the bandwidth of a sparse matrix as well as for the reduction of the cost of the associated Cholesky factorization. Our algorithms are inspired by the spectral method of Barnard, Pothen and Simon (1995), which derives a permutation for reducing the envelope-size of a sparse matrix by computing the second eigenvector of the associated Laplacian matrix. Two main modifications of that method are proposed and tested. The first is based on the experimental observation that it is often preferable to perform only few iterations of an iterative method converging to the second eigenvector; the second is the introduction of a weighted Laplacian. These simple ideas allow us to obtain a family of spectral methods that have been carefully tested on a set of matrices whose size ranges from few hundred to one million.
Starting Page	117
Ending Page	136
Page Count	20
File Format	PDF
ISSN	10171398
Journal	Numerical Algorithms
Volume Number	28
Issue Number	1-4
e-ISSN	15729265
Language	English
Publisher	Kluwer Academic Publishers
Publisher Date	2001-01-01
Publisher Place	Dordrecht
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Theory of Computation Numeric Computing Mathematics Algebra Algorithms
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics

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Heuristic Spectral Techniques for the Reduction of Bandwidth and Work-Bound of Sparse Matrices