derivative support

[jaeminoh]

Hello Professor Driscoll,

Do you have any plans to support derivative computation? (for real-valued functions)
There is an article on computing the derivatives of rational barycentric interpolants Schneider and Werner 1986.
If so, can I open a pull request?

Best regards,
Jaemin Oh

[nlw0]

I'm interested in that, do you have a patch already? How do I compute the derivative at a node?

[jaeminoh]

Hi @nlw0,

I just created a Gist, which is a copy from one of my private repositories. Please be careful since it hasn't been tested. I guess the first r argument of functions is the aaa result.

[tobydriscoll]

It's something I want to get to soon. In some early experimentation, I observed that the Schneider and Werner method can be unstable very close to interpolation nodes, but I have not looked into it systematically yet.

[tobydriscoll]

I have created a branch for derivatives that seems to be working. You should be able to take derivative(r) for any interpolant r.

Try add RationalFunctionApproximation#derivative and let me know how it goes.

[tobydriscoll]

Derivatives are merged in. The numerical stability is still not well understood.