高斯塞德尔迭代法c++

高斯塞德尔迭代法是一种求解线性方程组的迭代方法，其基本思想是通过不断迭代逼近方程组的解。下面是一个简单的 C++ 实现：

#include <iostream>
#include <cmath>

using namespace std;

const int MAXN = 100;
const double eps = 1e-6;

double a[MAXN][MAXN], b[MAXN];
double x[MAXN];

int main()
{
    int n;
    cout << "请输入方程组的未知数个数：";
    cin >> n;

    cout << "请输入增广矩阵：\n";
    for (int i = 1; i <= n; i++) {
        for (int j = 1; j <= n + 1; j++) {
            cin >> a[i][j];
        }
    }

    // 高斯塞德尔迭代
    double err = 1e9;
    while (err > eps) {
        err = 0;
        for (int i = 1; i <= n; i++) {
            double tmp = b[i];
            for (int j = 1; j <= n; j++) {
                if (i != j) {
                    tmp -= a[i][j] * x[j];
                }
            }
            x[i] = tmp / a[i][i];
            err += fabs(x[i] - b[i]);
            b[i] = x[i];
        }
    }

    cout << "方程组的解为：\n";
    for (int i = 1; i <= n; i++) {
        cout << "x" << i << " = " << x[i] << endl;
    }

    return 0;
}