Dan Christensen wrote:

> Well, in a computation in quantum gravity, I have the C code shown

> below. It has exactly 20 nested for loops! There are of course

> other ways to write it, but given the number of iterations, speed

> is the bottom line. Unfortunately, this is only the simplest test

> case of a larger problem...
You might want to have a look at:

http://amath.colorado.edu/pub/wavele...ers/pnas.ps.gz
The approach outlined here is a fairly generic framework to tackle

high-dimensionality problems, there's another preprint with more examples

coming down the pipeline.

With d=20, since your complexity for truly nested stuff goes like N^d you are

hosed for almost any value of N. Combining the ideas from the paper above

with:

http://amath.colorado.edu/pub/wavelets/papers/car.ps.gz
it is possible to write separated forms of many interesting kernels in

mathematical physics, providing algorithms which scale linearly with d (albeit

with big constants in front).

I'd like to know in a bit more detail what the context of your calculation is,

and whether the 20 comes from looping over dimesionalities of some

string-derived model or something else. We're very interested in finding

contexts where these dimesionality-reduction approaches may be used. While my

background is not in quantum gravity, if you keep the discussion generic enough

I should be able to follow (keep it bounded by general relativity, the standard

model and introductory stringy stuff and I should be fine).

Feel free to contact me directly at fperez AT colorado DOT edu if you don't feel

like talking about quantum gravity on c.l.py

Regards,

f