实验5插值实验.doc

年级、专业09级信息与计算科学姓名学号名单序号
实验时间2011年12月1日Matlab版本
注：实验报告的最后一部分是实验小结与收获
实验报告（5）：插值实验（Interpolation）

2011秋数学实验基础
实验报告（5）PageofNUMPAGES3

(1)WriteaMATLABfunctiontoperformtheLagrangianformInterpolation.
functiony=eg1_1
x=[46,49,51,52,54,56,57,58,59,60,61,62,63,64,66,67,68,71,72,71];
y=[40,50,55,63,72,70,77,73,90,93,96,88,99,110,113,120,127,137,132,137];
p=polyfit(x,y,3)
xi=46:0.5:72;
yi=polyval(p,xi)

(2)Writeacallbackm-filetocheckthefunctionyouwrite.
p=
-0.00170.3275-16.9037291.3741
ans=
Columns1through15
40505563727077739093968899110113
Columns16through20
120127137132137

Inthefollowingtable
(savedinthedatafilenamedInterpolation_Problem1_data.xls),XistheFahrenheit（华氏的）temperature,andYisthenumberoftimesacricket（蟋蟀）chirps（鸣叫）inoneminute.
Makeascatterplot(散点图)ofthedata.
>>x=[46,49,51,52,54,56,57,58,59,60,61,62,63,64,66,67,68,71,72,71];
>>y=[40,50,55,63,72,70,77,73,90,93,96,88,99,110,113,120,127,137,132,137];
>>plot(x,y,'o')
>>grid

Interpolatethedatawithsomeloworderpiecewiseinterpolatingpolynomials.
>>x=[46,49,51,52,54,56,57,58,59,60,61,62,63,64,66,67,68,71,72,71];
>>y=[40,50,55,63,72,70,77,73,90,93,96,88,99,110,113,120,127,137,132,137];
>>p=polyfit(x,y,3)
p=
-0.00170.3275-16.9037291.3741
>>xi=46:0.5:72;
>>yi=polyval(p,xi);
>>plot(x,y,'o',xi,yi,'k')
>>grid

Fitthedatabyusingan18th-degreepolynomialthatpassingthrough（通过）thedatapointsasanempiricalmodel.Analyzetheappropriatenessofdoingso.

ObservationNumberxyObservationNumberxy1464011619624950126288351551363994526314641105547215661136567016671207577717681278587318711379599019721321060932071137>>x=[46,49,51,52,54,56,57,58,59,60,61,62,63,64,66,67,68,71,72,71];
>>y=[40,50,55,63,72,70,77,73,90,93,96,88,99,110,113,120,127,137,132,137];
>>p=polyfit(x,y,18);
>>xi=46:0.5:72;
>>yi=polyval(p,xi);
>>plot(x,y,'o',xi,yi,'k')
>>grid

用18阶多项式拟合数据，画出的图像能够使尽量多的点落在图线上，更接近真实数据。

3．(Optional)
(1)WriteaMATLABfunctiontoperformtheLagrangianformInterpolationinsymbolicway.
(2)Writeacallbackm-filetocheckthefunctionyouwrite.

小结与收获：
这次作业让我进一步