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1、踏药席三當衣摩（威海）MATLAB课程论文学号：110610207姓名：矫同浩教师：曲荣宁日期：2013年06月01日1.用y(t)=t2ej5tsint生成一组较稀疏的数据，并用一维数据插值的方法对给出的数据进行曲线拟合，并将结果与理论曲线相比较。【求解】市下血的语句可以立即得出一组数据，这些数据分布情况如图所示。»t=0:0.2:2;y=t.A2.*exp(-5*t).*sin(t);plot(t,y,'o')»ezplotCt.A2.*exp(-5*t).*sin(t)[0,2]);holdonx1=0:0.01:
2、2;yl=interpl(t,y,x1,'spline');plot(xl,yl)2.试用分段三次样条函数和B样条函数对其进行拟合，并求出它们相应函数的数值导数。【求解】相应的三次样条插值和B■样条插值原苗数与导数函数分别如图所示。»x=[・2,・1.7,-1.4,-1」,・().&-0.5,-0.2,0.1,0.4,0.7,1,1.3,...1.6,1.9,2.2,2.5,2.8,3.1,3.4,3.7,4,4.3,4.6,4.9];y=[0.10289,0.11741,0.13158,0.14483,0.15656,0
3、.16622,0.17332,…0.1775,0.17853,0.17635,0.17109,0.16302,0.15255,0.1402,...0.12655,0.11219,0.09768,0.08353,0.07019,0.05786,0.04687,...0.03729,0.02914,0.02236];S=csapi(x,y);Sl=spapi(6,x,y);fnplt(S);holdon;fnplt(Sl)»Sd=fnder(S);Sdl=fnder(S1);fnplt(Sd),holdon;fnplt(Sdl
4、)函数拟合函数导数三次样条插值和B-样条插值拟合效杲原始数据不能直接用于样条处理，因为meshgrid()函数产生的数据格式与要求的ndgrid()函数不一致，所以需要对数据进行处理，其中需要的x和y均应该是向量，而z是原來z矩阵的转置，所以用下面的语句可以建立起三次样条和B■样条的插值模型，函数的表面图分别如图所示，口J见二者得出的结果很接近。»[x,y]=meshgrid(0:0.1:1.1);z=[0.83041,0.82727,0.82406,0.8209&0.81824,0.8161,0.81481,0.8146
5、3,0.81579,0.81853,0.82304;0.83172,0.83249,0.83584,0.84201,0.85125,0.86376,0.87975,0.89935,0.92263,0.94959,0.9801;0.83587,0.84345,0.85631,0.87466,0.89867,0.9284,0.96377,1.0045,1.0502,1.1,1.1529;0.84286,0.86013,0.88537,0.91865,0.95985,1.0086,1.0642,1.1253,1.1904,1.2
6、57,1.3222;0.85268,0.88251,0.92286,0.97346,1.0336,1.1019,1.1764,1.254,1.3308,1.4017,1.4605;0.86532,0.91049,0.96847,1.0383,1.118,1.2046,1.2937,1.3793,1.4539,1.5086,1.5335;0.88078,0.94396,1.0217,1.1118,1.2102,1.311,1.4063,1.4859,1.5377,1.5484,1.5052;0.89904,0.98276,1
7、.082,1.1922,1.3061,1.413&1.5021,1.5555,1.5573,1.4915,1.346;0.92006,1.0266,1.1482,1.2768,1.4005,1.5034,1.5661,1.5678,1.4889,1.3156,1.0454;0.94381,1.0752,1.2191,1.3624,1.4866,1.5684,1.5821,1.5032,1.315,1.0155,0.62477;0.97023,1.1279,1.2929,1.4448,1.5564,1.5964,1.5341
8、,1.3473,1.0321,0.6126&0.14763];»x0=[0.0:0」:1];yO=xO;z=z';S=csapi({xO,yO},z);fnplt(S)figure;S1=spapi({5,5},{xO,yO},z);fnplt(S1)o0三次样条B-样条三次样条插值和B・样条插值拟合效
