newton.cpp

常用数值算法的C++源码

#include "stdio.h"
#include "math.h"
#define   N 10000

int    flag=1;
double Function(double x);

double Newton(double x0,double e)
{
	int    counter=0;
	double x,y0,y1;
	double temp=e+1;
	flag=1;
	while(temp>e)
	{
		if(counter>N)
		{
			flag=0;
			printf("Newton序列发散\n");
			break;
		}
		y0=Function(x0);
		y1=Function(x0-y0);
		x=x0-pow(y0,2)/(y0-y1);
		temp=fabs(x-x0);
		x0=x;
		counter++;
	}
	return x;
}

double Function(double x)
{
	double y=pow(x,3)/3-x;
	return y;
}

/*
void main()
{
	int    i=1;
	double x0,x,delt;
	double e=0.5*pow(10,-5);
	while(flag)
	{
		x0=0.01*i;
        x=Newton(x0,e);
		if(fabs(x)>e) flag=0;
		if(flag) 
		{
            delt=0.01*i;
			printf("初值为%.2f时，解得x=%f\n",delt,x);
			i++;
		}
	}
	delt=0.01*i;
	printf("使Newton序列收敛于根x2的最大区间为：(-%f,%f)\n",delt,delt);
}*/


void main()
{
	double x0[7]={-100,-5,-0.7,0.3,0.7,7,100};
	double e=0.5*pow(10,-5);
	double x;
	for(int i=0;i<7;i++)
	{
		printf("x0=%f时,",x0[i]);
		x=Newton(x0[i],e);
		if(flag) printf("Newton序列收敛于%f\n",x);
    }
}