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Polynomial Root Clustering

✍ Scribed by T.A. Bickart; E.I. Jury

Publisher: Elsevier Science
Year: 1979
Tongue: English
Weight: 536 KB
Volume: 308
Category: Article
ISSN: 0016-0032
DOI: 10.1016/0016-0032(79)90055-3

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✦ Synopsis

A sequence of tests on derived polynomials to be strictly Hurwitz polynomials is shown to be equivalent to a given (typically real) polynomial having all its zeros

in an open sector, symmetric with respect to the real axis, in the left half-plane. 7'he number of tests needed is at most 1 + [(In k)/(ln 3)1, w h ere k is the integer associated with the central angle r/k of the sector. An extension of this result on the sector as a region of root clustering is given which shows that only a limited number of tests are needed to verify that the roots are clustered in a region composed as the intersection of a set of primative (sector-like) regions. The results reported evolve from application of a collection of mappings on the complex plane defined by a particular collection of Schwarz-Christoflel transformations.

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