数学毕业论文-什么样的连续函数能由整系数多项式逼近

上传者：网友
|

翻新时间：2023-03-16

收藏到账号

全屏

数学毕业论文-什么样的连续函数能由整系数多项式逼近

什么样的连续函数能由整系数多项式逼近

摘要：本文主要译自[1]，它系统地讨论了什么样的连续函数能由整系数多项式逼近，有以下两种情形：

（1）区间长度大于等于4的区间上，能由整系数多项式逼近的连续函数是这些整系数多项式本身；

（2）在区间长度严格小于4的区间上，连续函数能被整系数多项式1致逼近当且仅当在插值多项式为整系数多项式.

关键词：逼近;整系数多项式;插值多项式;代数整数.

What Can Be Approximated by Polynomials with Integer Coefficients

Abstract: This article is mainly translated from [1].What can be approximated by polynomials with integer coefficients is given in the following two aspects:

(1)If the interval has length four or more than the only functions that are approximable on the interval by polynomials with integer coefficients are these polynomials themselves.

(2) If is a continuous function on an interval I of length strictly less then 4,then is approximable on the interval by polynomials with integer coefficients if and only if its interpolating polynomial on has integer coefficients.

Keywords: approximation; polynomial with integer coefficients; interpolating polynomial; algebraic integer.

中文摘要 …………………………………………………………………………………………1

英文摘要 …………………………………………………………………………………………1

前言 ………………………………………………………………………………………………2

1 1些符号与专用术语…………………………………………………………………………2

2 区间长度大于等于4时整系数多项式逼近问题………………………………………………2

3 区间与上的整系数多项式逼近问题 ………………………………………………………4

4 区间长度小于4时的整系数多项式逼近问题…………………………………………………9

4.1代数整数及其相关概念 ………………………………………………………………………10

4.2插值多项式 ……………………………………………………………………………………10

5 结束语 …………………………………………………………………………………………15

6 参考文献 ………………………………………………………………………………………16