问题描述
x =
1
2
3
y =
4
5
6
ans =
2.2857
Matlab如何找到该结果? (我搜索了许多论坛，但我不明白他们讲的是什么.我想知道给出此结果的算法.)
How did Matlab find that result ? (I searched many forums but I did not understand what they told.I would like to know the algorithm which gave this result.)
推荐答案
来自\的MATLAB文档:
From MATLAB documentation of \:
如果A是具有M < or > N的M-by-N矩阵，而B是具有M个分量的列向量，或者是具有多个此类列的矩阵，则X = A\B是下划线或下划线的最小二乘解.方程组A*X = B的超定系统.
If A is an M-by-N matrix with M < or > N and B is a column vector with M components, or a matrix with several such columns, then X = A\B is the solution in the least squares sense to the under- or overdetermined system of equations A*X = B.
在这里，您的系统不是欠佳/超额预定的.由于两者都有3行.因此，您可以将方程式可视化为:
Here your system is not under/over-determined. Since both have 3 rows. So you can visualize your equation as:
xM=y
M=inv(x)*y
现在，由于矩阵不是正方形，它将使用SVD计算伪逆.因此，
Now, since your matrix is not square, it will calculate the pseudo-inverse using SVD. Therefore,
M=pinv(x)*y;
您将获得M的值为2.2857.
You will get value of M as 2.2857.
另一个解释可能是:它将以最小二乘的形式为您提供xM=y的解决方案.您可以按照以下步骤进行验证:
Another explanation can be: It will give you the solution of xM=y in the sense of least squares. You can verify this as follows:
M=lsqr(x,y)
这将为您提供M = 2.2857的值.
This will give you the value of M = 2.2857.
您始终可以在MATLAB命令窗口中执行help \以获得更多信息.
You can always do help \ in MATLAB command window to get more information.
鼓励您检查有关最小二乘和伪逆的更多详细信息.
You are encouraged to check more details about the least squares and pseudo-inverse.
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