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

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Tanouir Aloui 2021-6-26

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评论： Rondall 2024-3-17

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! :)

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Tanouir Aloui 2022-4-7

Thanks!

Rondall 2024-3-16

The automatically regularized solver, ARLS, has been available for nearly a year.

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Answer 1

Bjorn Gustavsson 2021-7-8

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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

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ayoub bouayaben 2022-4-5

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 2022-4-7

编辑：Tanouir Aloui 2022-4-7

@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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