Author(s): David H. Bailey and David J. Broadhurst

  Let $\{x_1, x_2, ..., x_n\}$ be a vector of real numbers. An integer relation
algorithm is a computational scheme to find the $n$ integers $a_k$, if they
exist, such that $a_1 x_1 + a_2 x_2 + ... + a_n x_n= 0$. In the past few years,
integer relation algorithms have been utilized to discover new results in
mathematics and physics. Existing programs for this purpose require very large
amounts of computer time, due in part to the requirement for multiprecision
arithmetic, yet are poorly suited for parallel processing. This paper presents
a new integer relation algorithm designed for parallel computer systems, but as
a bonus it also gives superior results on single processor systems. Single- and
multi-level implementations of this algorithm are described, together with
performance results on a parallel computer system. Several applications of
these programs are discussed, including some new results in number theory,
quantum field theory and chaos theory.

Paper: math.NA/9905048
Dated: Sun, 9 May 1999 15:10:46 GMT   (21kb)
Comments: 18 pages, LaTeX
Report-no: OUT--4102--79
Subj-class: Numerical Analysis; Scientific Computation; Mathematical Physics

URL: http://xxx.lanl.gov/abs/math/9905048