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Detection and Validation of Clusters of Polynomial Zeros

✍ Scribed by V. HRIBERNIG; H.J. STETTER

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
385 KB
Volume
24
Category
Article
ISSN
0747-7171

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✦ Synopsis

We consider the task of partitioning the zeros of a real or complex polynomial into clusters and of determining their location and multiplicity for polynomials with coefficients of limited accuracy. We derive computational procedures for the solution of this task which combine symbolic computation with floating-point arithmetic. The validation of the existence of m zeros in a specified small disk is described.

πŸ“œ SIMILAR VOLUMES

On the Location of the Zeros of a Polyno
On the Location of the Zeros of a Polynomial
✍ R.B. Gardner; N.K. Govil πŸ“‚ Article πŸ“… 1994 πŸ› Elsevier Science 🌐 English βš– 134 KB

The classical EnestΓΆm-Kekeya Theorem states that a polynomial \(p(z)=\) \(\sum_{i=0}^{n} a_{i} z^{\prime}\) satisfying \(0<a_{0} \leq a_{1} \leq \cdots \leq a_{n}\) has all its zeros in \(|z| \leq 1\). We extend this result to a larger class of polynomials by dropping the conditions that the coeffic