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On the Zeros of Polynomials of Best Approximation

✍ Scribed by Thomas Bloom; Jerzy Szczepański


Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
141 KB
Volume
101
Category
Article
ISSN
0021-9045

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Approximating the Number of Zeroes of a
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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 \(1-\delta\).

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## Abstract We prove that there is a universal measure on the unit circle such that any probability measure on the unit disk is the limit distribution of some subsequence of the corresponding orthogonal polynomials. This follows from an extension of a result of Alfaro and Vigil (which answered a qu