Regularized SVD to find the least square solution

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PNainwal
PNainwal 2023-9-2
评论： Rondall 2024-3-17
Hi all,
I am required to find a least square solution of system of linear equation (Ax = b) where the system is overdetermined. I notice that when i write A= vpa(A, 128) i get the full column rank whereas without vpa it is rank deficient matrix. I have used couple of mehods to solve this e.g
1 - x = A\b
2 - x = (A'*A\A'*b) ( produces the best ans so far but not perfect )
3 - x = pinv(double(A))*double(b)
4 - x = lsqminnorm(double(A'*A), double(A'*b))
but none of them seems to produce the solution i am wishing for. Kindly tell me other efficient ways of producing least square solution or let me know if i am going wrong.
  2 个评论
PNainwal
PNainwal 2023-9-2
So how can i can achieve that ? Is there a matlab function which does so ?Thanks

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采纳的回答

Bruno Luong
Bruno Luong 2023-9-2
移动：Bruno Luong 2023-9-2
There is no MATLAB function that I'm aware of, you can build your own or look in file exchange, there are few posted there.
The most basic Tikhonov regularization can be achieve with
lambda = something;
[m,n] = size(A)
x = [A; sqrt(lambda)*eye(n)] \ [b; zeros(n,1)]

更多回答（1 个）

Rondall
Rondall 2024-3-16
The new routine, ARLS, is for just such problems.
  2 个评论
Bruno Luong
Bruno Luong 2024-3-17
编辑：Bruno Luong 2024-3-17
Ran in:
R2023B
try
ARLS()
catch
arls()
end
Unrecognized function or variable 'arls'.
Rondall
Rondall 2024-3-17
Sorry.... I foolishly misspoke.... ARLS is available from File Exchange.... just seach F.E. for it.
It's NOT a built in function. My apologies.

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