Hi Jake,

On 2024-03-04 11:34:08, "Jake Bowhay" <jb9.bow...@gmail.com> wrote:
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.

That sounds like a great idea.

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.

I can't think of a much better home for it. `scipy.signal` is probably the domain where it is most used, but Padé is a fairly general method. I'd leave it where it is for now?

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.

Start with the implementation, and see whether the API looks different enough to warrant a whole new function. I skimmed the paper, and looks like there will be at least an added threshold parameter. But perhaps others too, in which case it might become worthwhile.

Thanks for working on this!

Stéfan
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