摘要
利用概率论中n重贝努利试验的相关结论,对函数逼近论中维尔斯特拉斯第一定理的证明过程进行分析,揭示了二者之间的联系.当f(x)在[0,1]上具有一阶连续导数时,给出了用多项式Bfn(x)=∑nk=0f(nk)xk(1-x)n-k逼近f(x)的逼近阶估计。
Using the conclusions of Beinoulli trials in probability, this paper analyzes the certifying process of the Weierstrass first theorem in approximation of functions and tells the relationship between them. When f (x) has continuous derivative at [ 0, 1 ], it gives a approximating order of the polynomial Bn^f(x)=↑∑k=0f(k/n)x^k(1-x)^(n-k).
出处
《贵州师范大学学报(自然科学版)》
CAS
2008年第1期93-95,共3页
Journal of Guizhou Normal University:Natural Sciences
关键词
维尔斯特拉斯定理
概率论
函数逼近
贝努利试验
逼近阶
Weierstrass theorem
probability
approximation of functions
Bernoulli trials
approximating order