Real zeros of classes of random algebraic polynomials
نویسندگان
چکیده
منابع مشابه
Real Zeros of Algebraic Polynomials with Dependent Random Coefficients
The expected number of real zeros of polynomials a0+a1x+a2x+ · · · + an−1xn−1 with random coefficients is well studied. For n large and for the normal zero mean independent coefficients, irrespective of the distribution of coefficients, this expected number is known to be asymptotic to (2/π) logn. For the dependent cases studied so far it is shown that this asymptotic value remains O(logn). In ...
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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 ...
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This paper provides an asymptotic estimate for the expected number of level crossings of a trigonometric polynomial TN (θ)= ∑N−1 j=0 {αN− j cos( j +1/2)θ + βN− j sin( j +1/2)θ}, where αj and βj , j = 0,1,2, . . . ,N − 1, are sequences of independent identically distributed normal standard random variables. This type of random polynomial is produced in the study of random algebraic polynomials w...
متن کاملOn Different Classes of Algebraic Polynomials with Random Coefficients
The expected number of real zeros of the polynomial of the form a0 a1x a2x · · · anx, where a0, a1, a2, . . . , an is a sequence of standard Gaussian random variables, is known. For n large it is shown that this expected number in −∞,∞ is asymptotic to 2/π logn. In this paper, we show that this asymptotic value increases significantly to √ n 1 when we consider a polynomial in the form a0 ( n 0 ...
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ژورنال
عنوان ژورنال: Journal of Applied Mathematics and Stochastic Analysis
سال: 2003
ISSN: 1048-9533,1687-2177
DOI: 10.1155/s1048953303000194