Affordable Access

Publisher Website

Polynomial Root Clustering

Authors
Journal
Journal of the Franklin Institute
0016-0032
Publisher
Elsevier
Publication Date
Volume
308
Issue
5
Identifiers
DOI: 10.1016/0016-0032(79)90055-3

Abstract

Abstract 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. The number of tests needed is at most 1 + ⌈( ln k)/( ln 3)⌉, where k is the integer associated with the central angle π/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-Christoffel transformations.

There are no comments yet on this publication. Be the first to share your thoughts.

Statistics

Seen <100 times
0 Comments

More articles like this

Regions of polynomial root clustering

on Journal of the Franklin Instit... Jan 01, 1977

Roots of composite polynomials—an application to r...

on Linear Algebra and its Applica... Jan 01, 1987

Root clustering of interval polynomials in the lef...

on Systems & Control Letters Jan 01, 1989

Symmetric and innerwise matrices for the root-clus...

on Journal of the Franklin Instit... Jan 01, 1972
More articles like this..