高斯消去法解方程组.cpp

数值分析中最常用的14个程序： 01_N皇后问题 01_循环赛程表 02_分段线性插值 02_牛顿插值法 03_构造正交多项式 03_最佳一致逼近多项式 04_简单迭代法求方程根[1

// 高斯消去法解方程组.cpp : Defines the entry point for the console application.
//

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


int main(int argc, char* argv[])
{
	cout << "  ****************************************" << endl;
    cout << "  **                                    **" << endl;
	cout << "  **         高斯消去法解方程组         **" << endl;
    cout << "  **                                    **" << endl;
	cout << "  ****************************************" << endl << endl;

	double B[3][4]={{-3,2,6,4},{10,-7,0,7},{3,-1,5,6}};	//增广矩阵
	int i,j,k,m;

	//消元过程
	for (i=0;i<2;i++)
	{
		double a;
		a=B[i][i];			
		for (j=i;j<4;j++)
			B[i][j]=B[i][j]/a;
		for (k=i+1;k<3;k++)
		{
			double b;
			b=B[k][i];
			if (b==0)
				continue;
			else
			{
				for (m=i;m<4;m++)
					B[k][m]=B[k][m]-b*B[i][m];
			}
			
		}
	}
	cout << "化简后的右上三角矩阵为：" << endl;
	for (i=0;i<3;i++)
	{
		for (j=0;j<4;j++)
			cout << B[i][j] << "  ";
		cout << endl;
	}
	cout << endl;

	//回代过程
	double X[3];	//方程组的解x1,x2,x3
	for (i=2;i>=0;i--)
	{
		for (j=i+1;j<3;j++)
			B[i][3]=B[i][3]-B[i][j]*X[j];
		X[i]=B[i][3]/B[i][i];
	}
	cout <<  "所求方程组的解为：";
	for (i=0;i<3;i++)
		cout << "x" << i+1 << "=" << X[i] << ", ";
	cout << endl;
	
	return 0;
}