bisection.cpp

二分法求一个未知数方程的根f(x)=0,x属于[a,b],除了显示每次计算的小区间外

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/////二分法求一个未知数方程的根f(x)=0,x属于[a,b]
/////改进：除了显示每次计算的小区间外，还根据给定的精度计算了所需的次数k
/////其中k>[log(b-a)-log(2*err)]/log(2);log=ln;
/////完善二分法的模块
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#include<iostream>
#include<math.h>
#include<iomanip>
using namespace std;
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double fun(double x);
void RootByBisection(double(*pf)(double x));
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int main()
{
	RootByBisection(fun);
	return 0;
}
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double fun(double x)
{
	return (x*x*x-x-1);
}
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void RootByBisection(double(*pf)(double x))
{
	double x1,x2,err;
	int flag;///记录迭代次数
	cout<<"请输入一元函数f(x)的定义域下界：a=";cin>>x1;
	cout<<"请输入一元函数f(x)的定义域上界：b=";cin>>x2;
	cout<<"请输入精度要求(推荐取err=1E-6)：err=";cin>>err;
	flag=static_cast<int>((log(x2-x1)-log(2*err))/log(2))+2;
	cout<<"预估：需计算的次数大约为："<<flag<<endl;
	cout.precision(10);
	cout<<endl<<"第0次的小区间为："<<"["<<setw(12)<<x1
		<<","<<setw(12)<<x2<<"]"<<endl;
	flag=0;
	while(fabs(x2-x1)>err)
	{
		if(pf(x1)*pf((x1+x2)/2)<0)
			x2=(x1+x2)/2;
		else
			x1=(x1+x2)/2;
		flag=flag+1;
		cout<<"第"<<flag<<"次的小区间为："<<"["<<setw(12)<<x1
		<<","<<setw(12)<<x2<<"]"<<endl;
	}
	cout<<endl<<"方程的近似根为：root="<<x1<<endl;
	cout<<"函数值f(root)="<<pf(x1)<<endl;
}
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