Regularized SVD to find the least square solution

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.

[Bruno Luong]

The code you cited none of them is regularized.

[PNainwal]

So how can i can achieve that ? Is there a matlab function which does so ?Thanks

Answer 1

[Bruno Luong]

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)]

[PNainwal]

Okay ! Thank you so much for reply.

Answer 2

[Rondall]

The new routine, ARLS, is for just such problems.

[Bruno Luong]

R2023B

try
    ARLS()
catch
   arls()
end

Unrecognized function or variable 'arls'.

[Rondall]

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.