lagrange.cpp

数值计算方法中的拉格朗日插值多项式的计算程序

//purpose:(x_i,y_i)的拉格朗日插值多项式     //
#include<stdio.h>
#define MAX_N 20                //定义(x_i,y_i)的最大维数
typedef struct tagPOINT         //点的结构
{
	double x;
	double y;
}
POINT;
int main()
{
	int n;
	int i,j;
	POINT points[MAX_N+1];
	double x,tmp,lagrange=0;
	printf("\ninput n value:");     //输入被插值点得数目
	scanf("%d",&n);
	if(n>MAX_N)
	{
		printf("the input n is larger than MAX_N,please redefine the MAX_N.\n");
		return 1;
	}
	if(n<=0)
	{
		printf("please input a number between 1 and %d.\n",MAX_N);
		return 1;
	}
	printf("now input the (x_i,y_i),i=0,...,%d:\n",n);//输入被插值点(x_i,y_i)
	for(i=0;i<=n;i++)
		scanf("%lf%lf",&points[i].x,points[i].y);
	printf("now input the x value:");                //输入计算拉格朗日插值多项式的x值
	scanf("%lf",&x);
	for(i=0;i<=n;i++)
	{
		for(j=0,tmp=1;j<=n;j++)
		{
			if(j==i)continue;
			tmp=tmp*(x-points[j].x)/(points[i].x-points[j].x);//tmp是拉格朗日基函数
		}
		lagrange=lagrange+tmp*points[i].y;
	}
	printf("lagrange(%f)=%f\n",x,lagrange);
	return 0;
}
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