【数值计算方法】雅可比解线性方程

废话少说，直接上干货。

#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#define MaxSize 100
double A[MaxSize][MaxSize]; //系数矩阵
double B[MaxSize];          //系数矩阵
double C[MaxSize][MaxSize]; //去对角线矩阵
double D[MaxSize][MaxSize]; //储存D逆
double E[MaxSize][MaxSize]; //储存-(D-1)*(L+U)
double F[MaxSize];          //(D-1)*B
double X[MaxSize];
double X1[MaxSize];
double Y[MaxSize];
#define e 1e-6 //10的负6次方
int n;        //矩阵尺寸大小

// 初始化矩阵
void InitMatrix()
{
    int i, j;
    for (i = 0; i < n; i++)
    {
        for (j = 0; j < n; j++)
        {
            if (i == j)
                D[i][j] = A[i][j];
            else
                C[i][j] = A[i][j];
        }
    }
}

// 雅可比迭代求解线性方程组
int Jacobi()
{
    int k;
    double sum, max_diff;
    for (k = 0; ; k++) 
    {
        max_diff = 0.0;
        for (int i = 0; i < n; i++)
        {
            sum = 0.0;
            for (int j = 0; j < n; j++)
            {
                if (j != i)
                    sum += A[i][j] * X[j];
            }
            X1[i] = (B[i] - sum) / A[i][i];
            double diff = fabs(X1[i] - X[i]);
            if (diff > max_diff)
                max_diff = diff;
        }
        for (int i = 0; i < n; i++)
            X[i] = X1[i];
        if (max_diff < e) // 满足精度要求退出循环
            break;
    }
    return k; // 返回迭代次数
}

// 输入系数矩阵和向量
void input()
{
    int i, j;
    printf("请输入系数矩阵A：\n");
    for (i = 0; i < n; i++)
        for (j = 0; j < n; j++)
            scanf_s("%lf", &A[i][j]);
    printf("请输入向量B：\n");
    for (i = 0; i < n; i++)
        scanf_s("%lf", &B[i]);
    printf("请输入初始向量X：\n");
    for (i = 0; i < n; i++)
        scanf_s("%lf", &X[i]);
}

// 打印方程组的近似解
void print()
{
    int i;
    printf("方程组的近似解：\n");
    for (i = 0; i < n; i++)
        printf("%lf\n", X[i]);
}

int main()
{
    printf("请输入矩阵行数：\n");
    scanf_s("%d", &n);
    printf("\n");
    input();
    InitMatrix();
    int N =Jacobi();
    print();
    printf("迭代次数为：%d",N);
    return 0;
}