AU - Farahmand, K.
TI - On Classifications of Random Polynomials
PT - JOURNAL ARTICLE
TA - srtc-jsri
JN - srtc-jsri
VO - 1
VI - 1
IP - 1
4099 - http://jsri.srtc.ac.ir/article-1-135-en.html
4100 - http://jsri.srtc.ac.ir/article-1-135-en.pdf
SO - srtc-jsri 1
ABĀ - Let $ a_0 (omega), a_1 (omega), a_2 (omega), dots, a_n (omega)$ be a sequence of independent random variables defined on a fixed probability space $(Omega, Pr, A)$. There are many known results for the expected number of real zeros of a polynomial $ a_0 (omega) psi_0(x)+ a_1 (omega)psi_1 (x)+, a_2 (omega)psi_2 (x)+ dots + a_n (omega)psi_n (x)$ where $ psi_j(x)$ , j=0.1.2...,n is a specific function of x. In this paper we highlight different characteristics arising for the random polynomial dictated by assuming different values for $ psi_j(x)$. Then we are able to classify random polynomials into three classes each of which share common properties. Although, we are mainly concerned with the number of real roots we also study the density of complex roots generated by assuming complex random coefficients for polynomials.
CP - IRAN
IN -
LG - eng
PB - srtc-jsri
PG - 1
PT - Research
YR - 2004