ACAC Seminar Abstract

ACAC Seminar Abstract

ACAC Seminars

ACAC Seminar Abstract

High-Precision Computation and Experimental Mathematics

Speaker: David H. Bailey
Date, Time: Fri, 04 Sep 2009 15:00

High-precision arithmetic has been called the "electron microscope" of experimental mathematics (the application of high-performance computing technology to research mathematics). The general approach is to compute some mathematical expression to very high precision (typically several hundred digits) for some specific choice of parameters, then apply an integer relation algorithm such as "PSLQ" to find a relation linking this object or expression and other known mathematical entities. Relations and formulas that are numerically discovered in this manner must then be proven rigorously.

One particularly fruitful area for this methodology is in the evaluation of definite integrals, such as those that arise in mathematical physics. Literally hundreds of new and intriguing results, specific and general, have been found in this manner, including results in Ising theory, quantum field theory and even computational biology. Progress in this arenas has been hampered by long run times required to evaluate high-dimensional integrals. However, with the increasing availability of highly parallel computer systems, many of these integrals can now be evaluated.

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