牛顿法.cpp

利用牛顿法解方程组

// 牛顿法.cpp : Defines the entry point for the console application.
//

#include "stdafx.h"
#include"math.h"
#include"iostream.h"
#include"iomanip.h"
#include"fstream.h"

class Niudun
{
protected:
	double **a;
	double **b;
	double **c;
	int xiangshu;
	double x0;
public:
	Niudun(char *file_name);
	double f_x(double);
	double f_x1(double);
	double f_x2(double);
	void diedai();
};
Niudun::Niudun(char *file_name)
{

	ifstream input(file_name);
	char m;
	if(!input)
		cout<<"con't open file"<<endl;
	else
	{
		input>>xiangshu;
		input>>x0;
		a=new double* [xiangshu];
		b=new double* [xiangshu];
		c=new double* [xiangshu];
		for(int i=0;i<xiangshu;i++)
		{
			a[i]=new double[2];
			b[i]=new double[2];
			c[i]=new double[2];
			input>>a[i][0];
			input.get(m);
			input>>a[i][1];
			b[i][0]=a[i][0];
			b[i][1]=a[i][1];
			c[i][0]=a[i][0];
			c[i][1]=a[i][1];
		

			b[i][0]*=b[i][1];
			b[i][1]-=1;

			c[i][0]*=c[i][1];
			c[i][1]-=1;
		
			c[i][0]*=c[i][1];
			c[i][1]-=1;

		}



	}
}

double Niudun:: f_x(double x)
{
	double y=0;

	for(int i=0;i<xiangshu;i++)
	{
		y+=a[i][0]*pow(x,a[i][1]);
	}

	return y;
}

double Niudun::f_x1(double x)
{
	double y=0;
	for(int i=0;i<xiangshu;i++)
	{

		y+=b[i][0]*pow(x,b[i][1]);
	}

	return y;
}
double Niudun::f_x2(double x)
{
	double y=0;
	for(int i=0;i<xiangshu;i++)
	{
		
		y+=c[i][0]*pow(x,c[i][1]);
	}

	return y;
}

void Niudun::diedai()
{
	int k=0;
	double x1;
    double f,g,h;
	do
	{
		x1=x0;
		f=f_x(x1)/f_x1(x1);
		g=1-f*f_x2(x1)/f_x1(x1);
		h=-f/g;
		x0=x1+h;
		k++;
	}while(fabs(h)>0.5e-10);

	cout<<"经过 "<<k<<"次循环"<<endl;
	cout<<setiosflags(ios::fixed)<<setprecision(10)<<"x="<<x0<<endl;

}


void main(int argc, char* argv[])
{
	Niudun niudun("a.txt");
	niudun.diedai();

	
}