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On the Zeroes of a Polynomial

✍ Scribed by H. Alzer

Publisher
Elsevier Science
Year
1995
Tongue
English
Weight
70 KB
Volume
81
Category
Article
ISSN
0021-9045

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πŸ“œ SIMILAR VOLUMES

On the Location of the Zeros of a Polyno
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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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Let \(P\_{N+1}(x)\) be the polynomial which is defined recursively by \(P\_{0}(x)=0\), \(P\_{1}(x)=1, \quad\) and \(\alpha\_{n} P\_{n+1}(x)+\alpha\_{n-1} P\_{n-1}(x)+b\_{n} P\_{n}(x)=x d\_{n} P\_{n}(x), \quad n=1, \quad 2, \ldots, N\), where \(\alpha\_{n}, b\_{n}, d\_{n}\) are real sequences with \(

Approximating the Number of Zeroes of a
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✍ M. Karpinski; M. Luby πŸ“‚ Article πŸ“… 1993 πŸ› Elsevier Science 🌐 English βš– 325 KB

We develop a probabilistic polynomial time algorithm which on input a polynomial \(g\left(x_{1}, \ldots, x_{n}\right)\) over \(G F[2], \epsilon\) and \(\delta\), outputs an approximation to the number of zeroes of \(g\) with relative error at most \(\epsilon\) with probability at least \(1-\delta\).