例1给出概率积分22fx=xdxx0（）e的数据表如表6.1所示，用不同的插值方法计算f(0.472)。表6.1概率积分数据表x0.460.470.480.49f(x)0.48465550.49375420.50274980.5116683x=0.46:0.01:0.49;%给出x，f(x)f=[0.4846555,0.4937542,0.5027498,0.5116683];formatlonginterp1(x,f,0.472)%用默认方法，即线性插值方法计算f(x)interp1(x,f,0.472,'nearest')%用最近点插值方法计算f(x)interp1(x,f,0.472,'spline')%用3次样条插值方法计算f(x)interp1(x,f,0.472,'cubic')%用3次多项式插值方法计算f(x)formatshort例2某检测参数f随时间t的采样结果如表5.1，用数据插值法计算t=2，7，12，17，22，17，32，37，42，47，52，57时的f值。表5.1检测参数f随时间t的采样结果t051015202530f3.10252.256879.51835.92968.84136.25237.9t35404550556065f6152.76725.36848.36403.56824.77328.57857.6T=0:5:65;X=2:5:57;F=[3.2015,2.2560,879.5,1835.9,2968.8,4136.2,5237.9,6152.7,...6725.3,6848.3,6403.5,6824.7,7328.5,7857.6];F1=interp1(T,F,X)%用线性插值方法插值F1=interp1(T,F,X,'nearest')%用最近点插值方法插值F1=interp1(T,F,X,'spline')%用3次样条插值方法插值F1=interp1(T,F,X,'cubic')%用3次多项式插值方法插值例3设z=x2+y2，对z函数在[0,1]×[0,2]区域内进行插值。x=0:0.1:1;y=0:0.2:2;[X,Y]=meshgrid(x,y);%产生自变量网格坐标Z=X.^2+Y.^2;%求对应的函数值interp2(x,y,Z,0.5,0.5)%在(0.5,0.5)点插值interp2(x,y,Z,[0.50.6],0.4)%在(0.5,0.4)点和(0.6，0.4)点插值interp2(x,y,Z,[0.50.6],[0.40.5])%在(0.5,0.4)点和(0.6，0.5)点插值%下一命令在(0.5,0.4),(0.6,0.4),(0.5,0.5)和(0.6,0.5)各点插值interp2(x,y,Z,[0.50.6]',[0.40.5])例4某实验对一根长10米的钢轨进行热源的温度传播测试。用x表示测量点(米)，用h表示测量时间(秒)，用T表示测得各点的温度(℃)，测量结果如表6.2所示。表6.2钢轨各点温度测量值Txh02.557.5100951400030884832126606764544841试用用3次多项式插值求出在一分钟内每隔10秒、钢轨每隔0.5米处的温度。x=0:2.5:10;h=[0:30:60]';T=[95,14,0,0,0;88,48,32,12,6;67,64,54,48,41];xi=[0:0.5:10];hi=[0:10:60]';temps=interp2(x,h,T,xi,hi,'cubic');mesh(xi,hi,temps);例5用一个3次多项式在区间[0，2π]内逼近函数xsin。X=linspace(0,2*pi,50);Y=sin(X);P=polyfit(X,Y,3)%得到3次多项式的系数和误差X=linspace(0,2*pi,20);Y=sin(X);Y1=polyval(P,X)plot(X,Y,':o',X,Y1,'-*')
