# 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.