Mean number of real zeros of a random trigonometric polynomial. III

Mean number of real zeros of a random trigonometric polynomial. III

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Article ID: iaor1997302
Country: United States
Volume: 8
Issue: 3
Start Page Number: 299
End Page Number: 317
Publication Date: Jul 1995
Journal: Journal of Applied Mathematics and Stochastic Analysis
Authors: ,
Keywords: root finding algorithm
Abstract:

If equ1 are independent, normally distributed random variables with mean 0 and variance 1, and if equ2 is the mean number of zeros on the interval equ3 of the trigonometric polynomial equ4, then equ5, in which equ6, equ7, equ8. After tabulation of equ9 values of equ10 when equ11, the authors find that the approximate formula for equ12, obtained from the above result when the error term is neglected, produces equ13 values that are in error by at most equ14 when equ15, and by only about 0.1% when equ16.

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