高斯赛德尔迭代法大家可以从网站上找到相关的公式推导，这里给出它的C++算法实现和运行的结果。

#include<iostream>
#include<math.h>
using namespace std;int n;                                                        //定义全局变量
double a[100][100], b[100], x[100][100];
double e;void input_func()
{for (int i = 0;i < n;i++){for (int j = 0;j < n;j++)                        //输入系数矩阵cin >> a[i][j];                              //输入等式右边的矩阵cin >> b[i];}
}void cal_func() {                                          //定义Gauss-Seidel迭代函数for (int k = 1;k <= 10;k++){for (int i = 0;i < n;i++){double s1 = 0, s2 = 0, s = 0;x[k][i] = 1.0 / a[i][i];double re = b[i];                            //每一行遍历完re重置for (int j = 0;j < n;j++){if (i < j)                               //上三角部分乘系数求和s1 += a[i][j] * x[k - 1][j];         else if(i > j)                           //下三角部分乘系数求和s2 += a[i][j] * x[k][j];}s = s1 + s2;                                //每一行遍历完求和re -= s;x[k][i] *= re;}for (int i = 0;i < n;i++)cout << x[k][i] << " ";cout << endl;       //输出第k遍迭代的X0、X1、X2bool judge = true;for (int i = 0;i < n;i++)if (fabs(x[k - 1][i] - x[k][i]) > e) {judge = false;break;}if (judge == true) return;}
}int main()
{cout << "系数输入矩阵的阶数" << endl;cin >> n;cout << "请输入系数矩阵" << endl;input_func();cout << "请输入初始向量" << endl;for (int i = 0;i < n;i++) cin >> x[0][i];cout << "输入求得的精度" << endl;cin >> e;cal_func();return 0;
}