scholarly journals Random polynomials with a prescribed number of real zeros

2002 ◽  
Vol 47 (3) ◽  
pp. 600-606
Author(s):  
L A Imhof ◽  
L A Imhof
Keyword(s):  
Random Polynomials ◽  
Real Zeros ◽  
Number Of Real Zeros

scholarly journals On real zeros of random polynomials with hyperbolic elements

1998 ◽  
Vol 21 (2) ◽  
pp. 347-350
Author(s):  
K. Farahmand ◽  
M. Jahangiri
Keyword(s):  
Asymptotic Estimate ◽  
Random Variables ◽  
Random Polynomials ◽  
Expected Number ◽  
Hyperbolic Polynomial ◽  
Asymptotic Value ◽  
Real Zeros ◽  
Number Of Real Zeros ◽  
Normally Distributed

This paper provides the asymptotic estimate for the expected number of real zeros of a random hyperbolic polynomialg1coshx+2g2cosh2x+…+ngncoshnxwheregj,(j=1,2,…,n)are independent normally distributed random variables with mean zero and variance one. It is shown that for sufficiently largenthis asymptotic value is(1/π)logn.

Expected Number of Real Zeros of Lévy and Harmonizable Stable Random Polynomials

2000 ◽  
Vol 7 (2) ◽  
pp. 379-386 ◽  
Author(s):  
S. Rezakhah ◽  
A. R. Soltani
Keyword(s):  
General Formula ◽  
Algebraic Polynomial ◽  
Stable Processes ◽  
Random Polynomials ◽  
Expected Number ◽  
Explicit Formulas ◽  
Real Zeros ◽  
Number Of Real Zeros ◽  
Stable Random Vector ◽  
Stable Noise

Abstract Assuming (A 0, A 1, . . . , An ) is a jointly symmetric α-stable random vector, 0 < α ≤ 2, a general formula for the expected number of real zeros of the random algebraic polynomial was obtained by Rezakhah in 1997. Rezakhah's formula is applied to the case where (A 0, . . . , An ) is formed by consecutive observations from the Lévy stable noise or from certain harmonizable stable processes, and more explicit formulas are derived for the expected number of real zeros of .

scholarly journals Random Trigonometric Polynomials with Nonidentically Distributed Coefficients

2010 ◽  
Vol 2010 ◽  
pp. 1-10
Author(s):  
K. Farahmand ◽  
T. Li
Keyword(s):  
Closed Form ◽  
Random Variables ◽  
Expected Value ◽  
Trigonometric Polynomials ◽  
Random Polynomials ◽  
Asymptotic Estimates ◽  
Expected Number ◽  
Real Zeros ◽  
Number Of Real Zeros ◽  
Normally Distributed

This paper provides asymptotic estimates for the expected number of real zeros of two different forms of random trigonometric polynomials, where the coefficients of polynomials are normally distributed random variables with different means and variances. For the polynomials in the form of and we give a closed form for the above expected value. With some mild assumptions on the coefficients we allow the means and variances of the coefficients to differ from each others. A case of reciprocal random polynomials for both above cases is studied.

Sign in / Sign up

Export Citation Format

Share Document