Albert Steppi

@fancidev. I’ll give more specific answers and advice in the PR message when I PR to your branch.

Nice work @fancidev. It looks like the series method is the way to go. I'm a bit curious though why your stopping criterion is `abs(w - w_) < tol`, involving...

> @steppi You’re definitely right. Here I’m being lazy and just wanted to code something quickly that works with `tol=0`, that’s how it becomes `abs(w-w_)

> 1. Using [Kahan summation](https://en.m.wikipedia.org/wiki/Kahan_summation_algorithm) (or `math.fsum`), the accuracy of the series method for this particular continued fraction is improved close to that of backward recursion, and hopefully within a...

I finally had some time to look into this. This is looking pretty good, but I don't think you're going to be able to get away with only using the...

For $v \approx 0.5$ and small $x$ you can just do `(ive(v-1, x) - ive(v, x))/ive(v-1, x)`. I'd suggest trying to find the region where the direct calculation `(ive(v-1, x)...

Thanks for all of the effort you've put into this @fancidev. > Which choice would you prefer? @steppi I think it's fine to restrict to $\nu >= 1$, since the...

@fancidev, I've found that the `double_double` arithmetic currently doesn't compile in NVRTC so I've removed the `iv_ratio` test case from `text_xsf_cuda.py` here https://github.com/scipy/scipy/pull/21210/commits/124f12e2c6859817f438d7f4af81855df0831c79. It's not really an issue since we...

> I’d like to help make it work but I don’t have an NVidia graphics card to test it. Or maybe it is possible to “cross compile”? Let me check...

> Will it really? To me, it's a pure math thing: eigenvalues of a real matrix are complex-valued. They can --- by accident --- have zero imaginary parts. These zero...