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Random polynomials

โœ Scribed by Kambiz Farahmand

Publisher
Elsevier Science
Year
1990
Tongue
English
Weight
206 KB
Volume
3
Category
Article
ISSN
0893-9659

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โœฆ Synopsis

The behaviour of an algebraic and a trigonometric polynomial with real random coefficients is reviewed, and the number of times that the curves representing these polynomials cross any real line in the zy-plane is presented.

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In this paper we find the expected number of zero crossings for a general algebraic polynomial, \(\sum_{j=1}^{n} a_{j}\left(\alpha x^{j}+\beta x^{-j}\right)\), and a general hyperbolic polynomial, \(\sum_{j=1}^{n} a_{j}(\alpha \cosh j x+\beta \sinh j x)\), where \(\alpha\) and \(\beta\) are constant