hermite插值.cpp

数值计算的一些经典算法

#include<iostream.h>
#define F(x) (1/(1+25*(x)*(x)))
#define F1(x) -50*x/((1+25*x*x)*(1+25*x*x))
#define L(y,x0,x1,x2) ((y)-x1)*((y)-x2)/((x0-x1)*(x0-x2))
#define FA(y,x0,x1,x2) (1-2*(y-x0)*(1/(x0-x1)+1/(x0-x2)))\
                       *L(y,x0,x1,x2)*L(y,x0,x1,x2)*F(x0)
#define FB(y,x0,x1,x2) ((y-x0)*L(y,x0,x1,x2)*L(y,x0,x1,x2)*F1(x0))
#include<math.h>
#define N 2
#define M 200
double g(double x[],double y);
void error(double a[]);
void main()
{
    double x[33],a[201];
	for(int i=0;i<=N;i++)
		x[i]=-1+i*2./N;
    for(int j=0;j<=M;j++)
	{
		double t=g(x,(-1+j*2./M));
        a[j]=fabs(F(-1+j*2./M)-t);
	}
	error(a);
}
double g(double x[],double y)
{  
    for(int i=0;i<=N;i+=2)
		if(y>=x[i]&&y<=x[i+2]) break;
	double t=FA(y,x[i],x[i+1],x[i+2])+FA(y,x[i+1],x[i],x[i+2])\
             +FA(y,x[i+2],x[i],x[i+1])+FB(y,x[i],x[i+1],x[i+2])\
             +FB(y,x[i+1],x[i],x[i+2])+FB(y,x[i+2],x[i],x[i+1]);
	cout<<y<<","<<t<<endl;
	return t;   
}
void error(double a[])
{   double max=a[0];
    int t;
	for(int i=1;i<=M;i++)
		if(a[i]>=max) {max=a[i],t=i;}
	cout<<"N= "<<N<<'\t';
	cout<<"x= "<<-1+(t)*2./M<<'\t';
	cout<<"errorMax= "<<max<<endl;
}