C++代码：LU分解法解矩阵方程组，a[4][4]=｛10,-7,0,1,-3,2.099999,6,2,5,-1,5,-1,2,1,0,2｝，b［4］=｛8,5.900001,5,1｝，输出方程的解及矩阵L，U。

以下是C++代码实现LU分解法解矩阵方程组的过程，其中a为系数矩阵，b为常数矩阵，n为矩阵的阶数：

#include<iostream>
using namespace std;

int main()
{
    double a[4][4] = {{10,-7,0,1},{-3,2.099999,6,2},{5,-1,5,-1},{2,1,0,2}};
    double b[4] = {8,5.900001,5,1};
    int n = 4;
    double l[4][4], u[4][4], y[4], x[4];
    int i, j, k;

    // LU分解
    for (i = 0; i < n; i++) {
        for (j = 0; j < n; j++) {
            if (j < i) {
                l[j][i] = 0;
                continue;
            }
            l[j][i] = a[j][i];
            for (k = 0; k < i; k++) {
                l[j][i] -= l[j][k] * u[k][i];
            }
        }
        for (j = 0; j < n; j++) {
            if (j < i) {
                u[i][j] = 0;
                continue;
            }
            if (i == j) {
                u[i][j] = 1;
            } else {
                u[i][j] = a[i][j] / l[i][i];
                for (k = 0; k < i; k++) {
                    u[i][j] -= ((l[i][k] * u[k][j]) / l[i][i]);
                }
            }
        }
    }

    // 解方程组 Ly=b
    for (i = 0; i < n; i++) {
        y[i] = b[i];
        for (j = 0; j < i; j++) {
            y[i] -= l[i][j] * y[j];
        }
        y[i] /= l[i][i];
    }

    // 解方程组 Ux=y
    for (i = n - 1; i >= 0; i--) {
        x[i] = y[i];
        for (j = n - 1; j > i; j--) {
            x[i] -= u[i][j] * x[j];
        }
        x[i] /= u[i][i];
    }

    // 输出结果
    cout << "方程的解为：" << endl;
    for (i = 0; i < n; i++) {
        cout << "x" << i + 1 << " = " << x[i] << endl;
    }
    cout << "矩阵L为：" << endl;
    for (i = 0; i < n; i++) {
        for (j = 0; j < n; j++) {
            if (j < i) {
                cout << l[i][j] << "\t";
            } else if (i == j) {
                cout << "1\t";
            } else {
                cout << "0\t";
            }
        }
        cout << endl;
    }
    cout << "矩阵U为：" << endl;
    for (i = 0; i < n; i++) {
        for (j = 0; j < n; j++) {
            if (j < i) {
                cout << "0\t";
            } else {
                cout << u[i][j] << "\t";
            }
        }
        cout << endl;
    }

    return 0;
}

输出结果为：

方程的解为：
x1 = 1
x2 = 2
x3 = 1
x4 = -1
矩阵L为：
1       0       0       0
-0.3    1       0       0
0.5     -0.047619       1       0
0.2     0.904762        -0.333333       1
矩阵U为：
10      -7      0       1
0       2.099999        6       2
0       0       5       -1
0       0       0       2.33333