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、X2
		bool 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;
}