The classical Enestöm-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
On zero locations of predictor polynomials
✍ Scribed by Fermin S. V. Bazán; Licio H. Bezerra
- Publisher
- John Wiley and Sons
- Year
- 1997
- Tongue
- English
- Weight
- 93 KB
- Volume
- 4
- Category
- Article
- ISSN
- 1070-5325
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✦ Synopsis
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 must be analyzed. We present a linear algebra approach for determining the zero locations of predictor polynomials, which enables us to generalize some early results obtained by Kumaresan in the signal analysis field. We also present an analysis of zero locations for time series having multiple zeros.
📜 SIMILAR VOLUMES
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