@MichaelE2 Hmm, that might be a possible source of instability then; as I noted, the monomial to Chebyshev conversion can be badly conditioned if the degree is high enough. Of course, if the splitting is done, and the resulting pieces are low order polynomials, we (hopefully!) avoid this instability.

@MichaelE2 Yes, I think it's something that can be suggested to them, altho I'm not sure they'll prioritize this for now. We may indeed have to roll our own.

(I'm still looking for a question to apply the two-variable chebfun technique to. If I can't find one, I might just e-mail you what I have, and maybe you can offer suggestions/improvements.)

(BTW, do you have MATLAB?)

@J.M. I figure either they're on it already or it'll take more than one request. I'm thinking V10.5.16, in honor of Chebyshev's birthday. :)

Yes, I have MATLAB. I'm not very knowledgeable about it, tho.

@MichaelE2 I see; I was asking for this next question: have you already tried the actual chebfun software? I've been using it on and off, and I really should find time to study the code and see what can be brought into Mathematica (or possibly improved using functions Mathematica has but MATLAB doesn't).

@J.M. Ditto for me.

community.wolfram.com/groups/-/m/t/852622