On the number of real solutions of a random polynomial

[摘要] We obtain bounds as a function of n, for the number of real solutions of the random algebraic equation Sigma(j-0)(n)a(j)x(j) = K-n where the coefficients a(j)'s are independent random variables and K-n is a sequence of real numbers with suitably specified growth. Both cases of finite and infinite variances are considered. When all K-n are set to a constant K it is shown how these bounds on the number of real solutions are a decreasing function of K. (C) 1997 Academic Press.

[发布日期] 1997-09-01