niudun.cpp

计算方法中牛顿插值方法

//author  Duanjing
#include<iostream.h>
void main()
{   
	int n,i,j;
	float X[15];
	float D[15];
	float t,L;	
	char a;
	cout<<"输入插值多项式的次数n=";
	cin>>n;
    cout<<"输入节点Xi以及f(Xi):"<<endl;
	cout<<"节点个数在15个以内"<<endl;
	for(i=0;i<=n;i++)
	{  cout<<"X["<<i<<"]=";
	cin>>X[i];
	cout<<"f[X"<<i<<"]=";
	cin>>D[i];
	}
	i=1;
//计算均差
	for(;i<=n;i++)
	{
		if(i!=j)
		{
			for(j=n;j>=i;j--)
		{D[j]=(D[j]-D[j-1])/(X[j]-X[j-i]);}
		}
	   else                                                                           {continue;}
	}
	//计算插值
		do{
		cout<<"输入插值点t:"<<endl;
		cin>>t;
		 float p;
		 p=D[n];
		 L=1;
		 for(i=n-1;i>=0;i--)
		 {
			 p=D[i]+(t-X[i])*p;}
		 cout<<"(t,p)="<<"("<<t<<","<<p<<")"<<endl;
		 cout<<"继续计算吗?   按y继续,按其他任意键结束插值    ";
	     cin>>a;}while(a=='y');
         cout<<"牛顿插值结束!"<<endl;
}