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Author Pan, Victor
Source ACM Digital Library
Content type Text
Publisher Association for Computing Machinery (ACM)
File Format PDF
Language English
Subject Domain (in DDC) Natural sciences & mathematics ♦ Mathematics ♦ Algebra
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.
Description Affiliation: Lehman College, New York (Pan, Victor)
Age Range 18 to 22 years ♦ above 22 year
Educational Use Research
Education Level UG and PG
Learning Resource Type Article
Publisher Date 1998-12-01
Publisher Place New York
Journal ACM SIGSAM Bulletin (SIGS)
Volume Number 39
Issue Number 3
Page Count 1
Starting Page 87
Ending Page 87

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Source: ACM Digital Library