[CLN-list] Re: applicability of AGM and binsplit

Bruno Haible bruno at clisp.org
Tue Jan 22 11:58:43 CET 2008


Joerg Arndt wrote:
> binsplit wins routinely whenever applicable, mostly for its memory
> locality.  There are, however, things where (to my knowledge) no
> binsplit based algorithm can be used.  So it is fine to also know
> about the performance of the AGM.

To me it looks like the AGM is based on mathematical properties of
particular algebraic curves. Whereas binsplit is a general technique
that provides fast evaluation of any holonomic function (with algebraic
initial conditions at an algebraic point) at regular and even at singular
points. These are resuls from Joris van der Hoeven [1] (see the three papers
  Fast evaluation of holonomic functions
  Fast evaluation of holonomic functions near and in singularities
  Efficient accelero-summation of holonomic functions
there).

Bruno

[1] http://www.math.u-psud.fr/~vdhoeven/



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