Talk:Integer relation algorithm

crap

24.84.104.223, why dont you correct the article with a readable explanation, rather than rambling garbage? —Preceding unsigned comment added by 146.6.200.213 (talk) 20:36, 17 April 2009 (UTC)[reply]

Rambling garbage? Perhaps, but maybe not. The fact that you think so might indicate a lack of knowledge/understanding on your part. I don't really care about wikipedia, but if you do you might want to change the history to accurately reflect things.

The name HJLS is due to Ferguson and Bailey, the actual algorithm is due to Hastad, Just, Lagarias and Schnorr who called it the small integer relation algorithm. Their paper is easily found online.

PSLQ (with parameter gamma=sqrt(2)) and HJLS (with full reductions) are equivalent algorithms. The differences observed by Bailey are due to implementational choices (the bit on mathworld about the numerical instability being due to using the Gram-Schmidt process to construct the initial basis is a load of crap put forth by Bailey, it is due to the lack of full reductions by Hastad et al. in an effort to save time). You may wish to look up the work of Meichsner here.

Also, the page seems to suggest that the LLL algorithm was developed as an extension of Ferguson and Forcades generalized Euclidean algorithm. You may wish to look up the initial paper on LLL (yes, I know LLL can be used to find integer relations and that there are strong similarities between the algorithms).

Acronym?

What does PSLQ stand for? --Slashme (talk) 14:15, 11 August 2008 (UTC)[reply]

Ferguson and Bailey's 1992 paper says "This algorithm has been named “PSLQ,” since it is based on a partial sum of squares scheme like the PSOS algorithm, yet it can be efficiently implemented with a LQ (lower trapezoidal–orthogonal) matrix factorization". Gandalf61 (talk) 14:28, 11 August 2008 (UTC)[reply]