区间上连续函数用多式逼近的性态毕业设计.docVIP

区间上连续函数用多项式逼近的性态 摘 要：在实际的应用中，经常遇到这样的问题：为解析式子比较复杂的函数寻找一个多项式来近似代替它，并要求其误差在某种度量下意义下最小．这就是用多项式来逼近函数问题的研究 本文主要讨论了区间上连续函数用多项式逼近的性态．首先给出了在闭区间上连续函数用多项式逼近的相关结论——Weierstrass逼近定理，是Weierstrass于1885年提出的，这条定理保证了闭区间上的任何连续函数都能用多项式以任意给定的精度去逼近．通过引用Bernstein多项式和切比雪夫多项式给出了相应的证明．其次列出了Bernstein多项式以及由Bernstein算子推广得到的Kantorovich算子它们的概念、一些具体的性质以及推广和应用． 最后，引进推广到无穷区间上的S．Bernstein 关键词： Weierstrass逼近定理；Bernstein多项式；Kantorovich算子；S．Bernstein  Polynomial approximation of continuous functions on the interval property Abstract：In practical applications， often encounter this problem: to find a polynomial to approximate the more complex function of the analytical formula， and requested the minimum of the error is some kind of metric significance． This is the polynomial approximation function problems． This article focuses on the behavior of interval polynomial approximation of continuous functions． Firstly， the conclusions continuous function on a closed interval with a polynomial approximation - Weierstrass approximation theorem， is weierstrass 1885， which Article theorem guarantees of any continuous function on the closed interval can use polynomials to approximate any given accuracy． Through quoted the Bernstein multinomial and the Chebyshev multinomial has given the corresponding proof． Next has listed the Bernstein multinomial as well as the Kantorovich operator which obtains by the Bernstein operator promotion their concept， some concrete nature as well as the promotion and the application． Finally， the introduction promotes to the infinite sector in the S．Bernstein multinomial， further has studied in the infinite sector the continuous function the condition which approaches with the multinomial， and obtained the related conclusion． Key words：Weierstrass approximation theorem， Bernstein polynomials; Kantorovich operator; S．Bernstein polynomial; infinite interval  第1章 绪论 1 1．1 区间上连续函数用多项式逼近的性态研究的背景 1 1．2 区间上连续函数用多项式逼近的性态研究的意义 1 第2章 Weierstrass逼近定理的证明及应用 3 2．1 Weierstrass逼近定理的第一种证明 3 2．1．1