摘要
<正> 一、前 言 以随机变量为系数的随机代数方程 F_n(ω,t)=sum from n a_i(ω)t~i =0在假定a_i(ω)(i=1,2,3,…,n-1)为遵从标准正态分布N(0,1)的独立随机变量条件下,其实根个数的期望EN_F(ω)的估计,先后有文献(1)及其引用文献。
Abstract
In this paper, we proveTheorem Let Fn(ω,t) = be a random algebraic eguation, wherea1(ω) (i=0, 1,2,…,n-1) are independent Gaussian random variables with mean o and standard deviation 1, then for n≥2, we havesup[ENF(ω)-2/π1nn=inf [ENF(ω)-2/π1lnn]=1-2/π1n2≈0.558728…
王友菁.
随机系数代数方程实根个数期望的界[J]. 南京林业大学学报（自然科学版）. 1984, 8(03): 113-118 https://doi.org/10.3969/j.jssn.1000-2006.1984.03.017
Wang Youjing.
SUP[ENF (ω)2/πLn N] 0.6312…AND INF[ENF(ω)-2/πLn N]-The superior limit to the average number of real roots of a random algebraic equation[J]. JOURNAL OF NANJING FORESTRY UNIVERSITY. 1984, 8(03): 113-118 https://doi.org/10.3969/j.jssn.1000-2006.1984.03.017
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