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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! :)
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...).
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 on 16 Mar 2024
Try ARLS, a completely automatic regularizing solver.
It was added to MATLAB in 2023.
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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