龙贝格算法.cpp

Gauss,加速迭代,拉格朗日插值法,龙贝格算法,牛顿迭代算法

#include<iostream>
#include<math.h>

float fun(float x)
{
	return exp(-x*x);
}
float Romberg(float a,float b,float(*f)(float),float eps)
{
	int n=1,k;
	float h=b-a,x,temp;
	float T1,T2,S1,S2,C1,C2,R1,R2;
	T1=(b-a)/2*((*f)(a)+(*f)(b));
	while(1)
	{
		temp=0;
		for(k=0;k<=n-1;k++)
		{
			x=a+k*h+h/2;
			temp+=(*f)(x);
		}
		T2=(T1+temp*h)/2;
		if(fabs(T2-T1)<eps)return T2;
		S2=(T2+(T2-T1)/3;
		if(n==1){T1=T2;S1=S2;h/=2;n*=2;continue;}
		C2=(S2+(S2-S1)/15;
		if(n==2){C1=C2;T1=T2;S1=S2;h/=2;n*=2;continue;}
		R2=(C2+(C2-C1)/63;
		if(n==4){R1=R2;C1=C2;T1=T2;S1=S2;h/=2;n*=2;continue;}
		if(fabs(R2-R1)<eps)return R2;
		R1=R2;C1=C2;T1=T2;S1=S2;h/=2;n*=2;
	}
}
void main()
{
	float eps=;
	cout<<"R="<<Romberg()<<endl;
}