數(shù)值分析曲線擬合的最小二乘法-董安葳

數(shù)值分析第二次實(shí)驗(yàn)報(bào)告姓名：董安葳學(xué)號：5123119題目：曲線擬合的最小二乘法實(shí)驗(yàn)方法：根據(jù)書中最小二乘法的定義，自行設(shè)計(jì)算法編寫matlab函數(shù)文件zuixiaoerchengnihe.m，然后通過調(diào)用自己編寫的函數(shù)來解決實(shí)際問題。實(shí)驗(yàn)過程：1．實(shí)驗(yàn)代碼：zuixiaoerchengnihe.mfunctionzuixiaoerchengnihe(X,Y，n)%X,Y為實(shí)驗(yàn)數(shù)據(jù)，分別為兩個向量，由用戶輸入，n為所要求的擬合曲線的次數(shù)[b,a]=size(X);G=zeros(n+1,n+1);%法方程的矩陣Gd=zeros(n+1,1);%法方程的矩陣dforii=1:n+1forjj=ii:n+1forkk=1:a;G(ii,jj)=G(ii,jj)+X(1,kk)A(ii+jj-2);%通過循環(huán)計(jì)算矩陣G的上三角endG(jj,ii)=G(ii,jj);%矩陣G是對稱矩陣，所以下三角的值直接拷貝上三角的值endforpp=1:ad(ii,1)=d(ii,1)+Y(1,pp)*X(1,pp)Uii-1);%通過循環(huán)計(jì)算矩陣dendendjielun=(G"-1))*d%解法方程，輸出為擬合曲線的系數(shù)向量%將所得系數(shù)向量通過循環(huán)輸出將標(biāo)準(zhǔn)的擬合曲線方程輸出fprintf('f(x)=')forii=1:n+1fprintf([num2str(jielun(ii,1))'x''A'num2str(ii-1)])ifii~=n+1fprintf('+')endendfprintf('\n')2．調(diào)用方法和輸出結(jié)果：P95第十六題：0Y010305080CommandWindowHOMEPLOTSAPRSC:?Users?安蘭?Desktop0.91.93.03.95.0]>>zuixiaoerchengnihe(X?Y?1)jieluii=0.90001.90003.00003.90005.000010305080110]110-7.855022.2538f(x)=-7.855x"0+22.2538x?lA?lP950Y010305080CommandWindowHOMEPLOTSAPRSC:?Users?安蘭?Desktop0.91.93.03.95.0]>>zuixiaoerchengnihe(X?Y?1)jieluii=0.90001.90003.00003.90005.000010305080110]110-7.855022.2538f(x)=-7.855x"0+22.2538x?lA?lP95第17題:HOMEPLOTSAPRS"固厚AC:?Users?寶蒐?Desktop?CommandWindow?X=[1925313844]1925313844?￥=[19.032.349.073.397.8]19.000032.300049.000073.300097.8000>>zuikiaoerchengnihe(X,Y,2)jielun=0.68820.01930.0497f(x)=0.68818z"0+0.019301z"l