func1p3.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[]={0.4,0.5,0.6,0.7,0.8},ay[]={-.916291,-.693147,-.510826,-.356675,-.223144},x=0.54;
	int n=5;
	cout<<"The value at that point is: "<<LP(x,ax,ay,n)<<endl;
	cin>>n;
}

//运行结果：-0.616143
//真值：-0.616186；误差:0.000043; 理论误差限(由余项公式)：0.001029
//可见对于该函数y=ln x，多项式插值有着相当好的效果