Mikael Slevinsky
Mikael Slevinsky
Then it's not working correctly, since it's returning inverse square-roots.
Probably the zero-endpoint conditions are currently being encoded in the coefficients à la Dirichlet spaces.
We'd need to determine the necessary number of Chebyshev points. For `sign`, it comes from the ratio of minimal root separation & location to domain length (just need one point...
That's interesting (and I like it!), but I'll mention that it's a philosophical break from "every function is represented as a `Fun`", since now the user and/or developer decides when...
Ah, no roots!
It would have to be a special internal function anyway that asserts a sign, since roots is O(m^2)
Subdivision results in O(m^2), but algorithms such as FastPolynomialRoots.jl for symmetric (unitary) plus-rank-one are provably fast & backward stable. I bet that an FMM-accelerated `split_points_on_an_interval` could attain O(m) for simple...
Does subdivision + fast rank-structured Hessenberg eigensolvers = O(m)? @ajt60gaibb
EDIT above: subdivision + fast eval via FMM + fast rank-structured Hessenberg eigensolvers = O(m)?
Right, I remember now that you use `nudct` in chebfun, and there is an issue with fast evaluation too close to the endpoints.