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Location of zeros of polynomials

✍ Scribed by Chadia Affane-Aji; Neha Agarwal; N.K. Govil

Publisher
Elsevier Science
Year
2009
Tongue
English
Weight
444 KB
Volume
50
Category
Article
ISSN
0895-7177

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πŸ“œ SIMILAR VOLUMES

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Predictor polynomials are often used in linear prediction methods mainly for extracting properties of physical systems which are described by time series. The aforementioned properties are associated with a few zeros of large polynomials and for this reason the zero locations of those polynomials mu

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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

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✍ G. Schmeisser πŸ“‚ Article πŸ“… 2001 πŸ› Elsevier Science 🌐 English βš– 182 KB

Let f (z)=a 0 , 0 (z)+a 1 , 1 (z)+ } } } +a n , n (z) be a polynomial of degree n, given as an orthogonal expansion with real coefficients. We study the location of the zeros of f relative to an interval and in terms of some of the coefficients. Our main theorem generalizes or refines results due to