Hi all, I want to propose improvements to the current implementation of Padé approximants offered within SciPy. Currently, the method we offer solves a toeplitz system which is often highly ill-conditioned. This leads to spurious pole-zero pairs or Froissart doublets which means in practice often the implementation offered in SciPy is unusable. For example, I am interested in Padé approximations to the solution of the Volterra integro-differential equations. Here the method in SciPy quickly breaks down.
I would like to propose we replace our current method with a method based on the paper by Trefethen et al. [1]. This paper has quite a lot of citations and is already implemented in the popular Chebfun package. Hopefully, this part is fairly uncontroversial as it is a clear improvement to something we already offer. However, there are a couple of questions about adding this: 1. Location. Currently, our Padé approximation lives within scipy.interpolate. Clearly, this is not an interpolation method so this would be a good opportunity to think about if there is a better place for this to live. 2. Implement within the old signature or start again. It was suggested that it would be easier to start afresh and deprecate the old function. I think this would be preferable as we wouldn't be shackled by old design decisions. As ever, please feel free to join in the discussion either here or on the original issue [2]. Regards, Jake [1] https://people.maths.ox.ac.uk/trefethen/publication/PDF/2011_144.pdf [2] https://github.com/scipy/scipy/issues/20064 _______________________________________________ SciPy-Dev mailing list -- scipy-dev@python.org To unsubscribe send an email to scipy-dev-le...@python.org https://mail.python.org/mailman3/lists/scipy-dev.python.org/ Member address: arch...@mail-archive.com
