三次样条插值算法

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1、//三次样条插值算法#includevoidmain(){cout<<"输入节点个数:";intnum;cin>>num;intn=num-1;double*x=newdouble[num];double*y=newdouble[num];cout<<"按序依次输入各处节点及函数值"<>x[i]>>y[i];double*h=newdouble[num];for(i=0;i<=n-1;i++)h[i]=x[i+1]-x[i];double

2、*a1=newdouble[num];double*b1=newdouble[num];cout<<"请输入边界。按1输入第一种边界条件,按2输入第二种边界条件:";intpd;cin>>pd;if(pd==1){cout<<"按顺序输入两端点的微商:"<>k1>>k2;a1[0]=0;a1[n]=1;b1[0]=2*k1;b1[n]=2*k2;}else{cout<<"按顺序输入两端点的二阶微商:"<>t1>>t2;a1[0]=1;a1[n]=

3、0;b1[0]=3*(y[1]-y[0])/h[0];b1[n]=3*(y[n]-y[n-1])/h[n-1];}for(i=1;i<=n-1;i++){a1[i]=h[i-1]/(h[i-1]+h[i]);b1[i]=((1-a1[i])*(y[i]-y[i-1])/h[i-1]+a1[i]*(y[i+1]-y[i])/h[i])*3;}double*a2=newdouble[num];double*b2=newdouble[num];a2[0]=-a1[0]/2;b2[0]=b1[0]/2;for(i=1;i<=n;

4、i++){a2[i]=-a1[i]/(2+(1-a1[i])*a2[i-1]);b2[i]=(b1[i]-(1-a1[i])*b2[i-1])/(2+(1-a1[i])*a2[i-1]);}double*m=newdouble[n+2];m[n+1]=0;for(i=n;i>=0;i--){m[i]=a2[i]*m[i+1]+b2[i];}cout<<"输入所要求的点:"<>xx;for(i=0;i<=n-1;i++){if(x[i]<=xx&&xx<=x[i+1])break;}if(i

5、<=n-1){doublekk;kk=(1+2*(xx-x[i])/(x[i+1]-x[i]))*(xx-x[i+1])*(xx-x[i+1])*y[i]/(x[i]-x[i+1])/(x[i]-x[i+1])+(1+2*(xx-x[i+1])/(x[i]-x[i+1]))*(xx-x[i])*(xx-x[i])*y[i+1]/(x[i+1]-x[i])/(x[i+1]-x[i])+(xx-x[i])*(xx-x[i+1])*(xx-x[i+1])*m[i]/(x[i]-x[i+1])/(x[i]-x[i+1])+(xx

6、-x[i+1])*(xx-x[i])*(xx-x[i])*m[i+1]/(x[i+1]-x[i])/(x[i+1]-x[i]);cout<

7、定函数y=f(x)的函数表如下，边界条件s’(0.25)=1，s’(0.53)=0.6868,用三次样条插值算法求f(0.35)的近似值。x0.250.30.390.450.53y=f(x)0.50.54770.62450.67080.728程序运行结果如下：