數(shù)值分析課程設(shè)計報告

頁數(shù) 13 字?jǐn)?shù) 4133

摘要（中）：本文建立在數(shù)值分析的理論基礎(chǔ)上，能夠在Matlab環(huán)境中運(yùn)行，給出了理論分析、程序清單以及計算結(jié)果。更重要的是，還有詳細(xì)的對算法的框圖說明。首先運(yùn)用Romberg積分方法對給出定積分進(jìn)行積分，然后對得到的結(jié)果用插值方法，分別求出Lagrange插值多項(xiàng)式和Newton插值多項(xiàng)式，再運(yùn)用最小二乘法的思想求出擬合多項(xiàng)式，最后對這些不同類型多項(xiàng)式進(jìn)行比較，找出它們各自的優(yōu)劣。
Summary(Enlish):This essay is based on numerical analysis ,and could be operated in Matlab environment, including theroy analysis, program and results. What’s more, there are detailed diagram which shows how the algorithm works. It first uses the integrating method of Romberg , which is an improved trapezoidal integration, to solve the given definite integral,then we create Lagrange’s interpolation polynomial and Newton’s interpolation polynomial. And according to least square method, curve fitting polynomial is created. At the last part of the essay, we compare these different patterns of polynomial, founding their distinctive advantages and disadvantages.

主題詞：Romberg積分,插值方法,Langrange插值多項(xiàng)式,Newton插值多項(xiàng)式,擬合多項(xiàng)式

參考文獻(xiàn)：
① John H.Mathews,Kurtis D.Fink 著，陳渝等譯。Numerical Methods Using MATLAB (Third Edition) 北京：電子工業(yè)出版社.
② 張池平主編.計算方法.哈爾濱：哈爾濱工業(yè)大學(xué)出版社.
③ 王兵團(tuán)，桂文豪著.數(shù)學(xué)實(shí)驗(yàn)基礎(chǔ).北京：北方交通大學(xué)出版社.
④ 楊萬利等著.數(shù)值分析教程.北京：國防工業(yè)出版社.
⑤ 康曉東主編.數(shù)值算法與非數(shù)值算法. 北京：電子工業(yè)出版社