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/lp/association-for-computing-machinery/block-tridiagonalization-of-effectively-sparse-symmetric-matrices-yJ60mHT0lC
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- Publisher
- Association for Computing Machinery
- Copyright
- Copyright © 2004 by ACM Inc.
- ISSN
- 0098-3500
- DOI
- 10.1145/1024074.1024078
- Publisher site
- See Article on Publisher Site
Abstract
A block tridiagonalization algorithm is proposed for transforming a sparse (or "effectively" sparse) symmetric matrix into a related block tridiagonal matrix, such that the eigenvalue error remains bounded by some prescribed accuracy tolerance. It is based on a heuristic for imposing a block tridiagonal structure on matrices with a large percentage of zero or "effectively zero" (with respect to the given accuracy tolerance) elements. In the light of a recently developed block tridiagonal divide-and-conquer eigensolver Gansterer, Ward, Muller, and Goddard, III, SIAM J. Sci. Comput. 25 (2003), pp. 65--85, for which block tridiagonalization may be needed as a preprocessing step, the algorithm also provides an option for attempting to produce at least a few very small diagonal blocks in the block tridiagonal matrix. This leads to low time complexity of the last merging operation in the block divide-and-conquer method. Numerical experiments are presented and various block tridiagonalization strategies are compared.
Journal
ACM Transactions on Mathematical Software (TOMS) – Association for Computing Machinery
Published: Sep 1, 2004