func1p4.cpp

数值分析最常用的四十种算法

//Interpolate,using Langrang Methom

#include <iostream.h>

//Langrange polynomial
double LP(double x,double *ax,double *ay,int n)
{
	double sum=0,Tsum=1;
	int i,j;
	for (i=0;i<n;i++)
	{
		for (j=0;j<n;j++)
		{
			if (j!=i)
				Tsum=Tsum*(x-ax[j])/(ax[i]-ax[j]);
		}
		sum=sum+Tsum*ay[i];
		Tsum=1;
	}
	return sum;
}

void main()
{
	double ax[]={1,2,3,4,5,6,7,8,9,10,11,12},ay[]={12,234,34,-1,34,2,5,23,34,9,45,23},x1=6.5,x2=11.2;
	int n=12;
	cout<<"The value at 1st point is: "<<LP(x1,ax,ay,n)<<endl;
	cout<<"The value at 2nd point is: "<<LP(x2,ax,ay,n)<<endl;
	cin>>n;
}

//运行结果：p(6.5)=-2.5738,p(11.2)=112.379
//与表中原有数据比较,发现其偏离极其之大,Runge现象非常显著
//即使在离插值点靠近的点,p(6.01)=1.7629,p(11.01)=47.7551，变化幅度非常的大
//可见对于该函数，并不适用多项式高次插值