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平方根法 乔累斯基分解Cholesky_解线性方程组的直接解法

标签：计算方法实验

#include 
   
    #include 
    
     const int maxn = 15;int main(){    double a[maxn][maxn], b[maxn], y[maxn], x[maxn], l[maxn][maxn];    int n, sum;    freopen("sqrt.txt", "r", stdin);    scanf("%d", &n);    for(int i = 1; i <= n; i++){        for(int j = 1; j <= n; j++)  scanf("%lf", &a[i][j]);        scanf("%lf", &b[i]);    }    /*    for(int i = 1; i <= n; i++){        for(int j = 1; j <= n; j++)  printf("%10f", a[i][j]);        printf("%10f\n", b[i]);    }    */    for(int i = 1; i <= n; i++){  //算L: 对正定矩阵A分解，A = LL^T        sum = 0;        for(int k = 1; k <= i - 1; k++)  sum += (l[i][k] * l[i][k]);        l[i][i] = sqrt(a[i][i] - sum);        sum = 0;        for(int j = i + 1; j <= n; j++){            for(int k = 1; k <= i - 1; k++)  sum += (l[j][k] * l[i][k]);            l[j][i] = (a[j][i] - sum) / l[i][i];        }    }    for(int i = 1; i <= n; i++){  //求y: A = LL^T -> LL^Tx = b -> Ly = b        sum = 0;        for(int k = 1; k <= i - 1; k++)  sum += (l[i][k] * y[k]);        y[i] = (b[i] - sum) / l[i][i];    }    for(int i = n; i >= 1; i--){  //求x: L^Tx = y        sum = 0;        for(int k = i + 1; k <= n; k++)  sum += (l[k][i] * x[k]);        x[i] = (y[i] - sum) / l[i][i];    }    for(int i = 1; i <= n; i++)  printf("%10f\n", x[i]);    return 0;}
    
   

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