lglrchzh.cpp

C++写的数值计算方法中的拉格朗日插值方法程序

//purpose: Neville迭代插值

#include <stdio.h>
#define MAX_N 20    //定义（x-i,y-i）的伟大维数
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 Q[MAX_N+1][MAX_N+1];
	double x;
	printf("\nInput n value:");    //输入被插值点的数目
	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);   //插入点（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:");   //输入计算插值多项式的x值
	scanf("%lf",&x);
	for(i=0;i<=n;i++)
		Q[i][0]=points[i].y;
	for(i=1;i<=n;i++)
	{
		for(j=1;j<=n;j++)
		{
			Q[i][j]=((x-points[i-j].x)*Q[i][j-1]-(x-points[i].x)*Q[i-1][j-1])/(points[i].x-points[i-j].x);
		}//计算Q(i,j)
	}
    for(i=0;i<=n;i++)
	{
		for(j=0;j<=i;j++)
			printf("Q(%d,%d)=%f\n",i,j,Q[i][j]);
	}  //输出Q(i,j)
    printf("p(%f)=%f\n",x,Q[n][n]);
    return 0;
}