c++实现赛德尔迭代法求解方程组

下面是使用C++实现赛德尔迭代法求解n元线性方程组的代码：

#include <iostream>
#include <cmath>
using namespace std;

const int N = 3; //方程组未知数个数

int main()
{
    double a[N][N] = {{4, -1, 0}, {-1, 4, -1}, {0, -1, 4}}; //系数矩阵
    double b[N] = {7, 4, -7}; //常数列
    double x[N] = {0}; //初始解向量
    double x0[N] = {0}; //上一次的解向量
    double eps = 1e-6; //精度要求
    int k = 0; //迭代次数

    do
    {
        k++;
        for (int i = 0; i < N; i++)
        {
            double sum1 = 0, sum2 = 0;
            for (int j = 0; j < i; j++)
            {
                sum1 += a[i][j] * x[j];
            }
            for (int j = i + 1; j < N; j++)
            {
                sum2 += a[i][j] * x0[j];
            }
            x[i] = (b[i] - sum1 - sum2) / a[i][i];
        }
        double delta = 0;
        for (int i = 0; i < N; i++)
        {
            delta += (x[i] - x0[i]) * (x[i] - x0[i]);
            x0[i] = x[i];
        }
    } while (sqrt(delta) > eps);

    cout << "Solution:" << endl;
    for (int i = 0; i < N; i++)
    {
        cout << "x[" << i << "] = " << x[i] << endl;
    }
    cout << "Iterations: " << k << endl;

    return 0;
}

与C语言实现的代码基本相同，主要是用了C++的iostream库来输出结果。需要注意的是，赛德尔迭代只有在系数矩阵满足严格对角占优条件时才能保证收敛。否则可能会出现迭代不收敛的情况。