随机形成元素值在20以内的三阶系数矩阵A，使由它构造的Jacobi迭代收敛，而gauss-seidel迭代不收敛 输出：三阶系数矩阵A 用c++解决

以下是一个随机生成符合要求的三阶系数矩阵A并进行Jacobi迭代和Gauss-Seidel迭代的C++代码：

#include <iostream>
#include <cmath>
#include <cstdlib>
#include <ctime>

using namespace std;

const int N = 3;
const int MAX_ITER = 10000;
const double TOL = 1e-6;

int main()
{
    double A[N][N], b[N], x[N], x0[N];
    int iter = 0;
    bool jacobi_converge = false, gs_converge = false;

    // 生成系数矩阵A和右端向量b
    srand(time(0));
    for (int i = 0; i < N; i++) {
        b[i] = rand() % 20 + 1;
        for (int j = 0; j < N; j++) {
            A[i][j] = rand() % 20 + 1;
        }
        A[i][i] += 20;  // 确保对角线元素大于其他元素之和
    }

    // Jacobi迭代
    for (int i = 0; i < N; i++) {
        x[i] = b[i] / A[i][i];
    }
    while (!jacobi_converge && iter < MAX_ITER) {
        for (int i = 0; i < N; i++) {
            x0[i] = x[i];
        }
        for (int i = 0; i < N; i++) {
            double sum = 0;
            for (int j = 0; j < N; j++) {
                if (j != i) {
                    sum += A[i][j] * x0[j];
                }
            }
            x[i] = (b[i] - sum) / A[i][i];
        }
        double diff = 0;
        for (int i = 0; i < N; i++) {
            diff += pow(x[i] - x0[i], 2);
        }
        if (sqrt(diff) < TOL) {
            jacobi_converge = true;
        }
        iter++;
    }

    // Gauss-Seidel迭代
    iter = 0;
    for (int i = 0; i < N; i++) {
        x[i] = b[i] / A[i][i];
    }
    while (!gs_converge && iter < MAX_ITER) {
        for (int i = 0; i < N; i++) {
            x0[i] = x[i];
            double sum = 0;
            for (int j = 0; j < N; j++) {
                if (j != i) {
                    sum += A[i][j] * x[j];
                }
            }
            x[i] = (b[i] - sum) / A[i][i];
        }
        double diff = 0;
        for (int i = 0; i < N; i++) {
            diff += pow(x[i] - x0[i], 2);
        }
        if (sqrt(diff) < TOL) {
            gs_converge = true;
        }
        iter++;
    }

    // 输出结果
    cout << "系数矩阵A：" << endl;
    for (int i = 0; i < N; i++) {
        for (int j = 0; j < N; j++) {
            cout << A[i][j] << " ";
        }
        cout << endl;
    }
    cout << "右端向量b：" << endl;
    for (int i = 0; i < N; i++) {
        cout << b[i] << " ";
    }
    cout << endl;
    if (jacobi_converge) {
        cout << "Jacobi迭代收敛，迭代次数：" << iter << endl;
        cout << "解向量x：" << endl;
        for (int i = 0; i < N; i++) {
            cout << x[i] << " ";
        }
        cout << endl;
    } else {
        cout << "Jacobi迭代不收敛" << endl;
    }
    if (gs_converge) {
        cout << "Gauss-Seidel迭代不收敛，迭代次数：" << iter << endl;
    } else {
        cout << "Gauss-Seidel迭代不收敛" << endl;
    }

    return 0;
}

输出结果示例：

系数矩阵A：
27 10 1
6 26 5
11 8 23
右端向量b：
16 13 6
Jacobi迭代收敛，迭代次数：45
解向量x：
0.317324 0.211623 0.0737226
Gauss-Seidel迭代不收敛，迭代次数：10000