Experimental Mathematics and High-Performance Computing

David H Bailey, Lawrence Berkeley Lab

Abstract:

Recent developments in "experimental mathematics" have underscored the value of high-performance computing in modern mathematical research. The most frequent computations that arise here are high-precision (typically several-hundred-digit accuracy) evaluations of integrals and series, together with integer relation detections using the "PSLQ" algorithm. Some recent highlights in this arena include: (2) the discovery of "BBP"-type formulas for various mathematical constants, including pi and log(2); (3) the discovery of analytic evaluations for several classes of multivariate zeta sums; (4) the discovery of Apery-like formulas for the Riemann zeta function at integer arguments; and (5) the discovery of analytic evaluations and linear relations among certain classes of definite integrals that arise in mathematical physics. The talk will include a live demo of the "experimental mathematician's toolkit".

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