编写sor迭代法的通用c语言计算程序

SOR（Successive Over-relaxation）迭代法是一种加速求解线性方程组的数值方法，它通过调整迭代步长来提高收敛速度。下面是一个简单的通用C语言程序示例，用于SOR方法，假设我们有一个二维线性系统Ax = b：

#include <stdio.h>
#include <stdlib.h>
#define N 5 // 方程组的大小
#define relaxation_factor 1.5

// 线性方程组矩阵A和右侧向量b的初始化
double A[N][N] = {
    {2, 1, 0, 0, 0},
    {1, 2, 1, 0, 0},
    {0, 1, 2, 1, 0},
    {0, 0, 1, 2, 1},
    {0, 0, 0, 1, 2}
};
double b[N];

// SOR迭代函数
void sor(double (*matrix)[N], double *vector, double *result, double omega) {
    for (int i = 0; i < N; ++i) {
        double temp = vector[i];
        for (int j = 0; j < N; ++j) {
            if (i != j)
                temp -= matrix[i][j] * result[j];
        }
        result[i] = (1 - omega) * temp + omega / matrix[i][i] * b[i];
    }
}

// 主函数，设置初始猜测值并运行SOR迭代
int main() {
    // 初始化b向量
    for (int i = 0; i < N; ++i) {
        b[i] = 1;
    }

    // 设置初始猜测值
    double initial_guess[N];
    for (int i = 0; i < N; ++i)
        initial_guess[i] = 0;

    // 迭代直到达到预设精度或其他停止条件
    double current_error = 1e9, last_error;
    int iterations = 0;
    while (current_error > 1e-6 && iterations < 1000) {
        sor(A, initial_guess, initial_guess, relaxation_factor);
        last_error = current_error;
        current_error = 0;
        for (int i = 0; i < N; ++i) {
            current_error += pow(initial_guess[i] - b[i], 2);
        }
        current_error = sqrt(current_error);
        iterations++;
    }

    printf("After %d iterations, the approximate solution is:\n", iterations);
    for (int i = 0; i < N; ++i) {
        printf("x[%d] = %.4f\n", i, initial_guess[i]);
    }

    return 0;
}