scholarly journals Expected number of real roots of random trigonometric polynomials

2017 ◽  
Vol 127 (12) ◽  
pp. 3928-3942 ◽  
Author(s):  
Hendrik Flasche
Keyword(s):  
Trigonometric Polynomials ◽  
Expected Number ◽  
Real Roots ◽  
Number Of Real Roots

scholarly journals Number of real roots of a random trigonometric polynomial

1992 ◽  
Vol 5 (4) ◽  
pp. 307-313 ◽  
Author(s):  
K. Farahmand
Keyword(s):  
Trigonometric Polynomial ◽  
Expected Number ◽  
Real Roots ◽  
Identical Distribution ◽  
Random Trigonometric Polynomial ◽  
Number Of Real Roots ◽  
Normally Distributed

We study the expected number of real roots of the random equation g1cosθ+g2cos2θ+…+gncosnθ=K where the coefficients gj's are normally distributed, but not necessarily all identical. It is shown that although this expected number is independent of the means of gj, (j=1,2,…,n), it will depend on their variances. The previous works in this direction considered the identical distribution for the coefficients.

scholarly journals On the Lower Bound for the Number of Real Roots of a Random Algebraic Equation

2007 ◽  
Vol 2007 ◽  
pp. 1-8
Author(s):  
Takashi Uno
Keyword(s):  
Lower Bound ◽  
Algebraic Equation ◽  
Random Variables ◽  
Real Roots ◽  
Number Of Real Roots

We estimate a lower bound for the number of real roots of a random alegebraic equation whose random coeffcients are dependent normal random variables.

scholarly journals Asymptotic variance of the number of real roots of random polynomial systems

2018 ◽  
Vol 146 (12) ◽  
pp. 5437-5449 ◽  
Author(s):  
D. Armentano ◽  
J-M. Azaïs ◽  
F. Dalmao ◽  
J. R. León
Keyword(s):  
Asymptotic Variance ◽  
Polynomial Systems ◽  
Random Polynomial ◽  
Real Roots ◽  
Number Of Real Roots
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