From: msk@beta.hut.fi (Mikko S Kiviranta) Subject: Integer Relation Detection (was: Cost of the Fast Multipole...) Date: 15 Jun 2000 21:36:48 GMT Newsgroups: sci.physics.research Summary: [missing] In article <8i4t0n$vtt$1@nntp.hut.fi> msk@beta.hut.fi (Mikko S Kiviranta) writes: > The top 10 algorithms were, by the way: > >- Integer relation detection >- The Dantzig simplex method for LP >- Krylov subspace iteration >- The QR method for eigenvalues >- Quicksort >- The decompositional approach to matrix computation >- FFT >- Metropolis >- The Fortran I compiler >- The fast multipole algorithm The other 7 (except for the Fortran compiler) belong to the standard toolbox of an average physicist doing numerical work, I believe, but the Fast Multipole and Integer Relation algorithms at least I hadn't heard of before (they both appear to be quite recent developements). Especially utilization of the Integer Relation Detection algorithm, has (according to the CSE article) lead to discovery of some pretty cool algebraic relations, like: - The fact that the 3rd bifurcation point of the logistic map is actually a root of a 12th degree polynomial with simple integer constants, and a similar (but more complicated) result for the 4th bifurcation point. - Discovery of a formula which allows fast calculation of the n:th digit of Pi, without having to calculate the preceeding digits. - Discovery of a seven-letter alphabet, with four-letter words that somehow represent (I don't understand this stuff well enough) the finite part of certain 3-loop vacuum Feynmann diagrams in the QFT. There was a reference to hep-th/9803091 in the CSE article. Considering the fact that the effective algorithm was only discovered in -97, the Integer Relation Detection sounds like a very fruitful algorithm, well worthy for the 'top ten' title. (Just wanted to share what I find quite exciting a developement) Best regards, Mikko