// 構造正交多項式.cpp : Defines the entry point for the console application.
//

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

double f(double x)	//求函數(shù)值
{
	return x;
}

double sum(double a, double h, int n)	//求所有新節(jié)點的函數(shù)和
{
	int i;
	double s=0;
	for (i=0;i<n;i++)
		s=s+f(a+i*h+h/2);
	return s;
}

double D_abs(double i, double j)	//求絕對值
{
	if (i-j<0)
		return j-i;
	else
		return i-j;
}

int main(int argc, char* argv[])
{
	cout << "  *******************************************" << endl;
	cout << "  **                                       **" << endl;
	cout << "  **            構造正交多項式             **" << endl;
	cout << "  **                                       **" << endl;
	cout << "  *******************************************" << endl << endl;

	double a=0.25,b=1.0;
	double h=b-a;
	double e=0.000001;	//精度控制
	double T1=h*(1+f(b))/2;	//T1初始值
	double T2,a0;
	int n=1;

	while (1)	//迭代求解
	{
		T2=T1/2+h*sum(a, h, n)/2;
		if (D_abs(T2, T1)<e)
		{
			break;
		}
		T1=T2;
		n=n*2;
		h=h/2;
	}
	a0=T2/0.75;
    cout << "所求一階正交多項式為:" << endl;
	cout << "Q1(x)=x-" << a0 << endl;
	return 0;
}