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What does Matlab have to offer for ill-conditioned inverse problems?

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When solving for x in the linear problem Ax = b, there are regularization methods for solving (like Tikhonov for example) in the case when A is an ill conditioned matrix. In my case, pinv, lsqnonneg, deconvlucy as well as the naive solution with A\b all of them do not work. In python there are a module that has an iterative solution for Tikhonov regularization but in Matlab I wasn't able to find a similar function. Any help will be appreciated! :)
  3 Comments
Rondall
Rondall on 16 Mar 2024
The automatically regularized solver, ARLS, has been available for nearly a year.

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Accepted Answer

Bjorn Gustavsson
Bjorn Gustavsson on 8 Jul 2021
Have a look at the excellent regtools toolbox. It contains all sorts of regularization functions Tikhonov, damped sdv, maximum-entropy etc. It has been very useful to me - making it possible to solve small and medium-sized inverse problems of all sorts without having to write my own versions of these (1: large-size I've taken to mean too large to be solved with this tool, 2 zeroth-order Tikhonov is rather easy to solve when the problem is small enough to do an svd, but...).
HTH
  2 Comments
ayoub bouayaben
ayoub bouayaben on 5 Apr 2022
Does this toolbox contain also a nonlinear ill-posed problem ?. If not, could you please suggest me references where i can find a them ?
Thank you.
Tanouir Aloui
Tanouir Aloui on 7 Apr 2022
Edited: Tanouir Aloui on 7 Apr 2022
@Bjorn Gustavsson That is what I have been using since then! Thanks for sharing. However, professor Hansen mentioned that regtools is more suitable for large scale probmems.
@ayoub bouayaben It is for linear problems but you can find more intresting infos on his publications.

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More Answers (1)

Rondall
Rondall on 16 Mar 2024
Try ARLS, a completely automatic regularizing solver.
It was added to MATLAB in 2023.
  2 Comments
John D'Errico
John D'Errico on 16 Mar 2024
This is absolutely incorrect. It was NOT added to MATLAB.
It appears you posted it on the file exchange, a very different thing.

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