@non-Jedi, can you share how to do it? I already asked the project but the information I obtained was that it is not possible.
@mcreel, yes, the QR decomposition is better for an ill-conditioned matrix. However, integrating the QR decomposition is not straightforward as the code relies on some of the by-products of the sweep-operator (the Sum of Squared Errors) to compute the other statistics. So if I use different methods, I will have to calculate the statistics differently.
Nevertheless, Cholesky and QR decompositions appear to be better for handling ill-conditioned problems only up to a certain severity.
At the moment, I do not know several things:
- If there is a class of problem that can’t be solved by say Cholesky but could be solved by QR.
- Which problems the Penrose-inverse can solve, and how does it compare towards Cholesky or QR?
- In which situations it is necessary to use some regularization techniques (such as Tikhonov).
Hence for now, I am thinking to add the condition number (from Linear Algebra) so that it is easier for the user to understand if the problem is indeed ill-conditioned and how severely.
I will also ask the community in a different post their views on this topic, as I am not an expert here.