On the number of real solutions of a random polynomial
type: Item
instance of: scholarly article
title: On the number of real solutions of a random polynomial
zbMATH Open document ID: 0904.60034
published in: Journal of Mathematical Analysis and Applications
publication date: 1999-01-18T00:00:00Z
review text: The author considers the random algebraic equation \(\sum^n_{j=0} a_jx^j= K_n\) where the coefficients \(a_j\) are independent random variables and \(K_n\) is a sequence of real numbers with suitably specified growth. He relaxes the normality assumption for coefficients by considering a general distribution with finite or infinite variance and he obtains bounds, as a function of \(n\), for the number of real solutions of the equation rather than the asymptotic value derived for the expected number of solutions in the normal case.
Mathematics Subject Classification ID: 60G99
zbMATH DE Number: 1117625
author: Kambiz Farahmand
MaRDI profile type: Publication
full work available at URL: jmaa.1997.5530
OpenAlex ID: W2083528288
cites work: The Accuracy of the Gaussian Approximation to the Sum of Independent Variates
cites work: Q4722950
cites work: How many zeros of a random polynomial are real?
cites work: Fourier analysis of distribution functions. A mathematical study of the Laplace-Gaussian law
cites work: On the average number of real roots of a random algebraic equation
cites work: Real Zeros of Random Algebraic Polynomials
cites work: An approximate formula for the expected number of real zeros of a random polynomial
cites work: On the Number of Real Roots of a Random Algebraic Equation
cites work: An Inequality for Sums of Independent Random Variables
cites work: Q4405392
cites work: Q5720531
cites work: On the Lower Bound of the Number of Real Roots of a Random Algebraic Equation with Infinite Variance
cites work: An Asymptotic Expansion for the Expected Number of Real Zeros of a Random Polynomial
DOI: 10.1006/JMAA.1997.5530
Recommended article: On the number of real roots of random polynomials
Recommended article: Q5460969
Recommended article: Q4789196
Recommended article: Q4731924
Recommended article: On the real roots of a random algebraic polynomial
Recommended article: Q4038273
Recommended article: Q4366413
Recommended article: On the Number of Real Roots of a Random Algebraic Equation
Recommended article: On the upper bound of the number of real zeros of a random algebraic polynomial
Recommended article: On the Number of Real Zeros of Random Fewnomials
description: scientific article; zbMATH DE number 1117625