Re: What has become of John Maddock's implementation of the Remez algorithm for Chebychev approximation?

From: Kostas Savvidis (kotika98_at_[hidden])
Date: 2021-06-18 12:57:56

> On Jun 16, 2021, at 21:23, Joachim Wuttke via Boost <boost_at_[hidden]> wrote:
> 
> Is the difficulty with elliptic integrals discussed in any publication?

A very difficult subject. The "smoothness" and "parabolicity" of those is highly misleading.
I would not expect any kind of polynomials to approximate elliptic integrals very well
because the radius of convergence of normal power series for it is finite, and LESS THAN
the range of the argument.
  From my experience with these functions, I would substract an approximant based on a pole-zero product expansion
and build a polynomial approximand for the remainder.

A classic paper is Luke in 1968:
https://www.ams.org/journals/mcom/1968-22-103/S0025-5718-1968-0226825-3/S0025-5718-1968-0226825-3.pdf <https://www.ams.org/journals/mcom/1968-22-103/S0025-5718-1968-0226825-3/S0025-5718-1968-0226825-3.pdf>

Cheers,
Kostas