jacobi迭代法c语言代码

以下是Jacobi迭代法的C语言代码：

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

#define MAX_ITERATIONS 1000 //最大迭代次数
#define TOLERANCE 1.0e-6    //容差
#define N 3                 //方程组的未知数个数

void Jacobi(double A[][N], double b[], double x[]) {
    int i, j, k;
    double sum;

    double *x0 = (double *)malloc(N * sizeof(double)); //存储上一次迭代的结果

    for (k = 0; k < MAX_ITERATIONS; k++) {
        for (i = 0; i < N; i++) {
            sum = 0.0;
            for (j = 0; j < N; j++) {
                if (j != i) {
                    sum += A[i][j] * x0[j];
                }
            }
            x[i] = (b[i] - sum) / A[i][i];
        }

        //检查迭代是否收敛
        double error = 0.0;
        for (i = 0; i < N; i++) {
            error += fabs(x[i] - x0[i]);
        }
        if (error < TOLERANCE) {
            printf("Jacobi method converged after %d iterations.\n", k + 1);
            return;
        }

        //将本次迭代的结果存储到x0中，作为下一次迭代的初始值
        for (i = 0; i < N; i++) {
            x0[i] = x[i];
        }
    }

    printf("Jacobi method did not converge after %d iterations.\n", MAX_ITERATIONS);
    return;
}

int main() {
    double A[N][N] = {{4.0, -1.0, 0.0},
                      {2.0, 7.0, -2.0},
                      {0.0, -3.0, 5.0}};
    double b[N] = {2.0, -3.0, 7.0};
    double x[N] = {0.0};

    Jacobi(A, b, x);

    printf("The solution is:\n");
    for (int i = 0; i < N; i++) {
        printf("x[%d] = %f\n", i, x[i]);
    }

    return 0;
}

这里仅提供Jacobi迭代法的基本实现，实际使用中还需要考虑更多的细节，比如矩阵是否对称正定，是否需要设置初始值等问题。