数值分析中的简单迭代法求方程根问题（迭代公式为[sqrt(x+1)]）

// 简单迭代法求方程根.cpp : Defines the entry point for the console application.
//

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


int main(int argc, char* argv[])
{
	cout << "  *******************************************" << endl;
	cout << "  **                                       **" << endl;
	cout << "  **              简单迭代法               **" << endl;
	cout << "  **                                       **" << endl;
	cout << "  *******************************************" << endl << endl;

	cout << "求方程 x^2-1*x-1=0 在区间 [1.5,2] 上的实根" << endl;
	cout << "选取 x0=1.5 , 精度 e=0.0001" << endl;
	cout << "-------------------------------------------" << endl;

	double x=1.5;		//初始值为0
	double e=0.0001;	//精度

	cout << "X = [ " << x << ", ";
	while (1)	//迭代求解
	{
		double y;
		y=sqrt(x+1);
		if (y-x<e)
		{
			x=y;
			cout << y << " ]" << endl<< endl;
			break;
		}
		x=y;
		cout << x << ", ";
	}

	cout << "所求根的近似值为 " << x << endl;

	return 0;
}