用c语言设计函数用列主元高斯消去法、Jacobi 迭代法、Gauss-Seidel 迭代法解如下方程组输出方程组的解，输出矩阵 L 和 U

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首先，我们需要定义一个函数来实现列主元高斯消去法，Jacobi迭代法和Gauss-Seidel迭代法。下面是这个函数的代码实现：

#include <stdio.h>
#include <stdlib.h>
#include <math.h>

// 列主元高斯消去法
void gauss_elimination(double **A, double *b, int n, double *x) {
    int i, j, k, max_row;
    double max_elem, tmp;

    // 高斯消元
    for (k = 0; k < n - 1; k++) {
        max_elem = fabs(A[k][k]);
        max_row = k;
        for (i = k + 1; i < n; i++) {
            if (fabs(A[i][k]) > max_elem) {
                max_elem = fabs(A[i][k]);
                max_row = i;
            }
        }

        if (max_elem == 0) {
            printf("Error: Singular matrix!\n");
            return;
        }

        // 交换k行和max_row行
        for (j = k; j < n; j++) {
            tmp = A[k][j];
            A[k][j] = A[max_row][j];
            A[max_row][j] = tmp;
        }
        tmp = b[k];
        b[k] = b[max_row];
        b[max_row] = tmp;

        // 消元
        for (i = k + 1; i < n; i++) {
            tmp = A[i][k] / A[k][k];
            for (j = k + 1; j < n; j++) {
                A[i][j] = A[i][j] - tmp * A[k][j];
            }
            b[i] = b[i] - tmp * b[k];
        }
    }

    // 回带求解
    for (i = n - 1; i >= 0; i--) {
        for (j = i + 1; j < n; j++) {
            b[i] = b[i] - A[i][j] * x[j];
        }
        x[i] = b[i] / A[i][i];
    }
}

// Jacobi迭代法
void jacobi_iteration(double **A, double *b, int n, double *x, double eps) {
    int i, j, k;
    double *x_new = (double *)malloc(n * sizeof(double));
    double error;

    // 初始化
    for (i = 0; i < n; i++) {
        x_new[i] = x[i];
    }

    // 迭代
    for (k = 0; k < 10000; k++) {
        error = 0;
        for (i = 0; i < n; i++) {
            x[i] = b[i];
            for (j = 0; j < n; j++) {
                if (j != i) {
                    x[i] = x[i] - A[i][j] * x_new[j];
                }
            }
            x[i] = x[i] / A[i][i];
            error = fmax(error, fabs(x_new[i] - x[i]));
        }
        if (error < eps) {
            break;
        }
        for (i = 0; i < n; i++) {
            x_new[i] = x[i];
        }
    }

    free(x_new);
}

// Gauss-Seidel迭代法
void gauss_seidel_iteration(double **A, double *b, int n, double *x, double eps) {
    int i, j, k;
    double *x_new = (double *)malloc(n * sizeof(double));
    double error;

    // 初始化
    for (i = 0; i < n; i++) {
        x_new[i] = x[i];
    }

    // 迭代
    for (k = 0; k < 10000; k++) {
        error = 0;
        for (i = 0; i < n; i++) {
            x[i] = b[i];
            for (j = 0; j < n; j++) {
                if (j != i) {
                    x[i] = x[i] - A[i][j] * x[j];
                }
            }
            x[i] = x[i] / A[i][i];
            error = fmax(error, fabs(x_new[i] - x[i]));
            x_new[i] = x[i];
        }
        if (error < eps) {
            break;
        }
    }

    free(x_new);
}

// 输出矩阵L和U
void output_LU(double **A, int n) {
    int i, j;
    double **L = (double **)malloc(n * sizeof(double *));
    double **U = (double **)malloc(n * sizeof(double *));
    for (i = 0; i < n; i++) {
        L[i] = (double *)malloc(n * sizeof(double));
        U[i] = (double *)malloc(n * sizeof(double));
    }

    // LU分解
    for (i = 0; i < n; i++) {
        for (j = 0; j < n; j++) {
            if (i <= j) {
                U[i][j] = A[i][j];
                for (k = 0; k < i; k++) {
                    U[i][j] = U[i][j] - L[i][k] * U[k][j];
                }
                if (i == j) {
                    L[i][j] = 1;
                } else {
                    L[i][j] = 0;
                }
            } else {
                L[i][j] = A[i][j] / U[j][j];
                U[i][j] = 0;
            }
        }
    }

    // 输出L和U
    printf("L = \n");
    for (i = 0; i < n; i++) {
        for (j = 0; j < n; j++) {
            printf("%lf ", L[i][j]);
        }
        printf("\n");
    }
    printf("U = \n");
    for (i = 0; i < n; i++) {
        for (j = 0; j < n; j++) {
            printf("%lf ", U[i][j]);
        }
        printf("\n");
    }

    // 释放内存
    for (i = 0; i < n; i++) {
        free(L[i]);
        free(U[i]);
    }
    free(L);
    free(U);
}

// 测试主函数
int main() {
    double **A, *b, *x;
    int n, i, j;

    printf("请输入方程组的个数n：");
    scanf("%d", &n);

    // 初始化矩阵和向量
    A = (double **)malloc(n * sizeof(double *));
    b = (double *)malloc(n * sizeof(double));
    x = (double *)malloc(n * sizeof(double));
    for (i = 0; i < n; i++) {
        A[i] = (double *)malloc(n * sizeof(double));
        for (j = 0; j < n; j++) {
            printf("请输入矩阵A[%d][%d]的值：", i, j);
            scanf("%lf", &A[i][j]);
        }
        printf("请输入向量b[%d]的值：", i);
        scanf("%lf", &b[i]);
        x[i] = 0; // 初始化解向量
    }

    // 列主元高斯消去法求解
    gauss_elimination(A, b, n, x);
    printf("列主元高斯消去法求解结果：\n");
    for (i = 0; i < n; i++) {
        printf("x[%d] = %lf\n", i, x[i]);
    }

    // Jacobi迭代法求解
    jacobi_iteration(A, b, n, x, 1e-6);
    printf("Jacobi迭代法求解结果：\n");
    for (i = 0; i < n; i++) {
        printf("x[%d] = %lf\n", i, x[i]);
    }

    // Gauss-Seidel迭代法求解
    gauss_seidel_iteration(A, b, n, x, 1e-6);
    printf("Gauss-Seidel迭代法求解结果：\n");
    for (i = 0; i < n; i++) {
        printf("x[%d] = %lf\n", i, x[i]);
    }

    // 输出矩阵L和U
    output_LU(A, n);

    // 释放内存
    for (i = 0; i < n; i++) {
        free(A[i]);
    }
    free(A);
    free(b);
    free(x);

    return 0;
}

在这个函数中，我们首先定义了三个函数：`gauss_elimination`，`jacobi_iteration` 和 `gauss_seidel_iteration`，它们分别实现了列主元高斯消去法，Jacobi迭代法和Gauss-Seidel迭代法。然后，我们定义了一个输出矩阵L和U的函数`output_LU`。最后，在主函数中，我们输入了方程组的个数n，初始化了矩阵A和向量b，分别用列主元高斯消去法，Jacobi迭代法和Gauss-Seidel迭代法求解方程组，并输出了结果和矩阵L和U。

希望这个代码能够帮到您。