高斯消元法的应用

//执行环境是VC 6.0

//通过高斯消元法求解方程的解

//input：

// 2 5 8

// 9 2 12

//output:

// x1:1.073171

// x2:1.170732

//方程如下:

//{2x + 5y = 8

//{9x + 2y = 12

#include <stdio.h>

#include <stdlib.h>

void main( void )

{

int n, i, j, k;

double client, temp = 0.0;

double **a;

printf("输入方式如下(系数以0表示无),最后一排是B的值:\n");

printf("4 5 2 3 2 5\n");

printf("4 6 2 1 0 2\n");

printf("4 5 2 1 3 2\n");

printf("1 2 1 2 3 2\n");

printf("0 2 5 1 1 3\n");

printf("请输入未知量的个数:");

scanf("%d", &n);

printf("\n请输入系数矩阵和右端向量\n");

//分配内存空间

a = new double *[n];

for (i =0 ; i < n; i++)

a[i]= new double[n + 1];

//输入数据

for (i = 0; i < n; i++)

for (j = 0; j <= n; j++)

scanf("%lf", (*(a + i) + j));

for(k = 0; k < n - 1; k++)

for(i = k + 1; i < n; i++)

{

client = a[i][k]/a[k][k];

for(j = k + 1; j < n; j++)

a[i][j] = a[i][j] - client * a[k][j];

a[i][n] = a[j - 1][n] - client * a[k][n];

}

a[n - 1][n] = a[n - 1][n]/a[n - 1][n - 1];

for(i = n - 2; i >= 0; i--)

{

for (j = i + 1; j < n; j++)

temp += a[i][j] * a[j][n];

a[i][n] = (a[i][n] - temp) / a[i][i];

}

for(i = 0; i < n; i++)

printf("X%d = %lf\n", i + 1, a[i][n]);

}