On Thu, Oct 4, 2012 at 8:02 AM, Fredrik Johansson <[email protected]> wrote: > On Wed, Oct 3, 2012 at 2:12 AM, Ondřej Čertík <[email protected]> wrote: >> Hi, >> >> Does anyone have experience with implementing rational function >> approximations >> to a given special function of one variable? This would be extremely >> useful addition >> to sympy. Here is an example for the error function from the standard >> gfortran library: > > This is something I've needed quite frequently, but I've never been > bothered enough to code it myself. I usually just use Mathematica > (EconomizedRationalApproximation or MiniMaxApproximation). It would be > great to have in sympy or mpmath.
Yes, this is it --- we need these two functions. I didn't know that Mathematica had it, nice. I've been thinking how to automatically cover the whole interval let's say (0, oo) and I would simply pick "m, n", then start on (0, a), call EconomizedRationalApproximation, check the error, if it is lower than 1e-18 (absolute error and probably also some relative error), then increase "a". Once we have the maximum "a", we do the interval (a, b) and maximize "b". And so on. Ondrej -- You received this message because you are subscribed to the Google Groups "sympy" group. To post to this group, send email to [email protected]. To unsubscribe from this group, send email to [email protected]. For more options, visit this group at http://groups.google.com/group/sympy?hl=en.
