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

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Tanouir Aloui
Tanouir Aloui on 26 Jun 2021
Answered: Bjorn Gustavsson on 8 Jul 2021
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! :)

Answers (1)

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...).

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