第 1 页/共 7页数值计算实验—实验报告 2一、实验项目：第二类边界条件三次样条插值二、实验目的和要求a. 通过本实验深入地理解三次样条插值多项式的基本原理b. 通过数值算例更好的领会三次样条插值多项式具有较高的准确性三、实验内容1.用调试好的程序解决如下问题已知正弦函数表X.i0.50.70.91.11.31.51.71.9f.i0.47940.64420.78330.89120.96360.99750.99170.9463以及边界条件 S''(0.5)=0.4794,S''(1.9)=0.9463。用三次样条插值多项式 S(x)计算诸节点中点处的函数值，并将计算结果与 sinx 在相应点的数值相比较。计算结果(参考)u.i0.60.81.01.21.41.61.8s(u.)0.564620.717330.841440.932060.985470.999590.97386sinu.0.564640.717360.841470.932040.985450.999570.97385(1).程序n=8;p1=0.4794;pn=0.9463;u=[0.6,0.8,1.0,1.2,1.4,1.6,1.8];p=7;x=[0.5,0.7,0.9,1.1,1.3,1.5,1.7,1.9];y=[0.4794,0.6442,0.7833,0.8912,0.9636,0.9975,0.9917,0.9463];fori=1:n-1h(i)=x(i+1)-x(i);enda2(1)=1;g(1)=3*(y(2)-y(1))/h(1)-p1*h(1)/2;fork=2:n-1a1(k-1)=h(k)/(h(k)+h(k-1));a2(k)=h(k-1)/(h(k)+h(k-1));g(k)=3*a2(k)*(y(k+1)-y(k))/h(k)+3*a1(k-1)*(y(k)-y(k-1))/h(k-1);enda1(n-1)=1;g(n)=3*(y(n)-y(n-1))/h(n-1)+pn*h(n-1)/2;%追赶法求三转角方程b1(1)=2;第 2 页/共 7页m(l)=g(l)/2;b2(l)=a2(l)/bl(l);fori=2:nbl(i)=2-al(i-1)*b2(i-1);if(i~=n)b2(i)=a2(i)/b1(i);endm(i)=(g(i)-a1(i-1)*m(i-1))/b1(i);endfori=n-1：-1:1m(i)=m(i)-b2(i)*m(i+1);endforj=1:pfori=1:nif((u(j)>=x(i))&&(u(j)
