2011秋 实验报告(5)插值实验(Interpolation).doc

年级、专业 姓名 学号名单序号 实验时间 2011年 11月17日 Matlab版本 2010 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）1 (1)Write a MATLAB function to perform the Lagrangian form Interpolation. (2)Write a call back m-file to check the function you write.解：%函数文件的名字存为LagIn,主要利用了数值逼近中拉格朗日基函数的表达式 function f=LagIn(t,y)n=length(t);syms xw=1;for j=1:n w=w*(x-t(j);endf=0;for i=1:n l(i)=w/subs(diff(w,x,1),x,t(i)/(x-t(i); f=f+sum(l.*y);endf1=simplify(f);data=input(:);f=subs(f1,x,data)2 In the following table (saved in the data file named Interpolation_Problem1_data.xls), X is the Fahrenheit（华氏的） temperature, and Y is the number of times a cricket（蟋蟀） chirps（鸣叫） in one minute. (1) Make a scatterplot(散点图) of the data. (2) Interpolate the data with some low order piecewise interpolating polynomials. (3) Fit the data by using an 18th-degree polynomial that passing through（通过） the data points as an empirical model. Analyze the appropriateness of doing so.Observation NumberxyObservation Numberxy1464011619624950126288351551363994526314641105547215661136567016671207577717681278587318711379599019721321060932071137解：(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;plot(x,y,o)title();xlabel(x);ylabel(y);legend(Data point);(2) x=46 49 51 52 54 56 57 58 59 60 61 62 63 64 66 67 68 71 72;y=40 50 55 63 72 70 77 73 90 93 96 88 99 110 113 120 127 137 132;xi=47:0.25:70;yi=interp1(x,y,xi,spline);plot(x,y,o,xi,yi) (3) t=46 49 51 52 54 56 57 58 59 60 61 62 63 64 66 67 68 71 72;y=40 50 55 63 72 70 77 73 90 93 96 88 99 110 113 120 127 137 132;p = polyfit(t,y,18);xi=46:0.1:72;y1 = polyval(p,xi);plot(t,y,o,xi,y1)3(Optional)(1) Write a MATLAB function to perform the Lagrangian form Interpolation in symbolic way