NDLI: Polynomial root-finding with matrix eigen-solving

Content Provider	ACM Digital Library
Author	Pan, Victor
Abstract	Numerical matrix methods are increasingly popular for polynomial root-finding. This approach usually amounts to the application of the QR algorithm to the highly structured Frobenius companion matrix of the input polynomial. The structure, however, is routinely destroyed already in the first iteration steps. To accelerate this approach, we exploit the matrix structure of the Frobenius and generalized companion matrices, employ various known and novel techniques for eigen-solving and polynomial root-finding, and in addition to the Frobenius input allow other highly structured generalized companion matrices. Employing polynomial root-finders for eigen-solving is a harder task because of the potential numerical stability problems, but we found some new promising directions, particularly for sparse and/or structured input matrices.
Starting Page	87
Ending Page	87
Page Count	1
File Format	PDF
ISSN	01635824
DOI	10.1145/1113439.1113448
Journal	ACM SIGSAM Bulletin (SIGS)
Volume Number	39
Issue Number	3
Language	English
Publisher	Association for Computing Machinery (ACM)
Publisher Date	1998-12-01
Publisher Place	New York
Access Restriction	One Nation One Subscription (ONOS)
Content Type	Text
Resource Type	Article

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Polynomial root-finding with matrix eigen-solving