laq.cpp

一元三点不等距插值（此算法避免了拉格朗日算法的龙格现象）

// laq.cpp : Defines the entry point for the console application.
//

#include "stdafx.h"

int main(int argc, char* argv[])
{
	printf("Hello World!\n");
	return 0;
}

double laq(double *x,double *y,double u,int n)
{
	double v,h1,h2;
	int i,j,k;

	for(i=0;i<=n-1;i++)
	{
		if((u-x[i])*(u-x[i+1])<=0)
		{
			k=i;
			break;
		}
	}
	if(i==n)
	{
		if(fabs(u-x[0])<fabs(u-x[n]))
		{
			k=0;
		}
		else
		{
			k=n-1;
		}
	}
	if((k==n-1) || (k!=0 && fabs(u-x[k])<fabs(u-x[k+1])))
	{
		k--;
	}

	v=0;
	for(i=k;i<=k+2;i++)
	{
		h1=h2=1;
		for(j=k;j<=k+2;j++)
		{
			if(j!=i)
			{
				h1*=(u-x[j]);
				h2*=(x[i]-x[j]);
			}
		}
		v+=y[i] * (h1/h2);
	}
	return v;
}