Re: [問題] 最小方差解

[Append (<(￣︶￣)>)]

推 zhewei:\
→ zhewei:\是matlab幫你弄好的，不用\  也可以參考我po的網址來求解
推 Append:doc mldivide裡面有寫吧@___@""
推 YoursEver:預設是用QR分解來解,若考慮到condition number之類的問
→ YoursEver:題,可以查查Householder/Givens該怎麼寫. (Matlab)
→ waveken:如果他要求LSM 怎可能是用反矩陣就求解出來
→ waveken:除非他問錯問題 ! 或是他寫的方式讓大家誤解!
雖然確實不能算是反矩陣...不過就是這樣喔。=P
首先是解法。"/" (也就是mldivide)

mldivide at MATLAB Documentation
http://www.mathworks.com/access/helpdesk/help/techdoc/ref/mldivide.html

Least Squares Solutions
If the equation Ax = b does not have a solution (and A is not a square
matrix), x = A\b returns a least squares solution — in other words, a
solution that minimizes the length of the vector Ax - b, which is equal to
norm(A*x - b). See Example 3 for an example of this.
.
.
.
If A is not square, then Householder reflections are used to compute an
orthogonal-triangular factorization.
A*P = Q*R
where P is a permutation, Q is orthogonal and R is upper triangular (see qr).
The least squares solution X is computed with X = P*(R\(Q'*B))


Least Squares Solutions at Wolfram Mathworld
http://ppt.cc/sJAV

A general way to find a least squares solution to an overdetermined system is
to use a singular value decomposition to form a matrix that is known as the
pseudo-inverse of a matrix. In Mathematica this is computed with
PseudoInverse. This technique works even if the input matrix is rank
deficient. The basis of the technique is given below.

好這樣應該夠了。
有興趣的話，
Moore-Penrose Matrix Inverse at Wolfram Mathworld
http://ppt.cc/PhR~

順便說，MATLAB Documentation建議，
解這個問題的時候盡量不要生出inverse(喔當然這裡是pseudo-inverse)，
而是直接用"\"。
A frequent misuse of inv arises when solving the system of linear equations.
One way to solve this is with x = inv(A)*b.
A better way, from both an execution time and numerical accuracy standpoint,
is to use the matrix division operator x = A\b.

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另外，如果是我們真的誤解了的話，請放心的說出來。...




以上。=)

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推 waveken:我是猜的問題沒有那麼單純
→ waveken:應該是constrained linear least-squares problems
→ waveken:function lsqlin 之類的
→ waveken:某些值需要疊代 不然他直接說解反矩陣就好啦 !
→ waveken:所以我才說 可能他講錯 或講不夠詳細 !
→ waveken:不然就是他們老師故做玄虛拉 !
→ Append:...為什麼是他們老師? 我猜不出來這跟他們老師的關係...
→ Append:另外 一個星期以來我第一次看到你推文裡面有指引...
→ waveken:AX=B A,B是常數矩陣;僅X未知 那應該是我想太複雜了!
→ waveken:Append 問太簡單的 我還是沒回答吧 !
→ waveken:有的我做過or我會then我就指引拉!