最小二乘法.cpp

数值分析

#include<iostream.h>

void main()
{
	int n;
	float a0,a1;

	cout<<"输入结点个数:"<<endl;
	cin>>n;

	float *X=new float [n];
	float *f=new float [n];

	cout<<"输入x值:"<<endl;
	for(int i1=0;i1<=n-1;i1++)
		cin>>X[i1];
	cout<<"输入函数值:"<<endl;
	for(int i2=0;i2<=n-1;i2++)
		cin>>f[i2];

	float b0,b1,
		  b2,b3;//系数矩阵
	float c0,c1;//右侧矩阵

	//b0,b1,b2,b3的初始化
	b0=float(n);
	b1=X[0];
	for(int i3=1;i3<=n-1;i3++)
		b1=b1+X[i3];
	b2=b1;
	b3=X[0]*X[0];
	for(int i4=1;i4<=n-1;i4++)
		b3=b3+X[i4]*X[i4];

	//c0,c1的初始化
	c0=f[0];
	for(int i5=1;i5<=n-1;i5++)
		c0=c0+f[i5];
	c1=X[0]*f[0];
	for(int i6=1;i6<=n-1;i6++)
		c1=c1+X[i6]*f[i6];
	
	//result
	float temp0=b0*b3/b1-b2;
	float temp1=b0*b3/b2-b1;

	a0=(b0*c0/b1-c1)/temp0;
	a1=(b0*c1/b2-c0)/temp1;
	
	cout<<"y="<<a0<<"+"<<a1<<"X"<<endl;
}