Random polynomials
type: Item
instance of: scholarly article
title: Random polynomials
zbMATH Open document ID: 0708.60065
DOI: 10.1016/0893-9659(90)90011-Y
author: Kambiz Farahmand
published in: Applied Mathematics Letters
publication date: 1990-01-01T00:00:00Z
review text: The author studies several interesting differences of the behaviour between the algebraic and trigonometric curves. He shows that the trigonometric curves on an average oscillate more frequently than the algebraic ones and that the number of K level-crossings of the trigonometric curves is the same as for x-axis crossings which for the algebraic case decreases as K increases. He also shows that changing zero mean to a non-zero mean will not affect the number of crossings of trigonometric curves whereas in the case of algebraic curves, it is reduced by half. He also obtains a formula for the expected number of crossings using the Kac-Rice formula.
Mathematics Subject Classification ID: 60H99
zbMATH DE Number: 4163854
zbMATH Keywords: K level-crossings
zbMATH Keywords: trigonometric curves
zbMATH Keywords: Kac-Rice formula
MaRDI profile type: Publication
cites work: Q5544740
cites work: On the average number of real roots of a random algebraic equation
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cites work: Q4403533
cites work: On the Average Number of Real Roots of a Random Algebraic Equation (II)
cites work: Q5773312
cites work: Mathematical Analysis of Random Noise
full work available at URL: 0893-9659(90)90011-y
OpenAlex ID: W4213280408
description: scientific article; zbMATH DE number 4163854