Real Zeros of Random Algebraic Polynomials with Binomial Elements
نویسنده
چکیده
This paper provides an asymptotic estimate for the expected number of real zeros of a random algebraic polynomial a0 + a1x + a2x + ···+ an−1xn−1. The coefficients aj ( j = 0,1,2, . . . ,n− 1) are assumed to be independent normal random variables withmean zero. For integers m and k = O(logn)2 the variances of the coefficients are assumed to have nonidentical value var(aj) = ( k−1 j−ik ) , where n = k ·m and i = 0,1,2, . . . ,m− 1. Previous results are mainly for identically distributed coefficients or when var(aj)= (n j ) . We show that the latter is a special case of our general theorem.
منابع مشابه
Algebraic Polynomials with Random Coefficients with Binomial and Geometric Progressions
The expected number of real zeros of an algebraic polynomial ao a1x a2x · · · anx with random coefficient aj , j 0, 1, 2, . . . , n is known. The distribution of the coefficients is often assumed to be identical albeit allowed to have different classes of distributions. For the nonidentical case, there has been much interest where the variance of the jth coefficient is var aj ( n j ) . It is sh...
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