Question

MATLAB 编程计算 高手请进。小弟感激不尽！

A=[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 1/2 0 1/2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1/2 0 0 0 1/2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 1/2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1/2
0 0 0 0 0 0 1/2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1/2
0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1/2 0 0 0 1/2 0
0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0
0 0 0 1/2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1/2 0 0 0 0
0 0 0 1/2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1/2 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0
0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ]
注：A是一个24x24矩阵 B是A的转置矩阵
B=A'
e=[1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]
C=e'*e/24
D=0.5*B+0.5*C
F=DX 其中X的初始值 是一个24个元素都为1的列向量
反复迭代计算F=DX ，直至F向量的值等于X列向量的值 即计算结果收敛
求 结果收敛时的 X 列向量 以及编程

Answer 1

下面是matlab命令代码，你直接复制到matlab命令窗口，回车运行就可以（你愿意的话作成函数代码也可以）：
************************
A=[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 1/2 0 1/2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1/2 0 0 0 1/2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 1/2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1/2
0 0 0 0 0 0 1/2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1/2
0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1/2 0 0 0 1/2 0
0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0
0 0 0 1/2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1/2 0 0 0 0
0 0 0 1/2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1/2 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0
0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ];
B=A';
e=[1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1];
C=e'*e/24;
D=0.5*B+0.5*C;
X=e';
k=0;%循环步数，防止死循环。
t=1;%判断F和X是否对应相等的辅助变量。
while(t<24 && k<=10000)
t=0;
X=F;
F=D*X;
for i=1:24
if(F(i)==X(i))
t=t+1;
k=k+1;
end
end
end
F
X

*****************************************
（精度你还可以自己调的）
结果：
>> F

F =

0.9375
0.6250
0.5000
2.6340
2.7368
0.5000
0.6250
0.5000
0.6562
1.0781
1.5391
1.8867
1.2344
0.5000
0.5000
0.5000
0.5000
0.9687
1.5896
1.2358
0.5000
0.5000
0.9717
0.7812

>> X

X =

0.9375
0.6250
0.5000
2.6340
2.7368
0.5000
0.6250
0.5000
0.6562
1.0781
1.5391
1.8867
1.2344
0.5000
0.5000
0.5000
0.5000
0.9687
1.5896
1.2358
0.5000
0.5000
0.9717
0.7812