Computer Science

Colloquium Details

Experimental Mathematics and High-Performance Computing

Abstract

The field of high-performance computing has been very successful in enabling an ever-growing number of important scientific applications to be performed on high-end computer systems. Hardware advances, algorithm improvements, parallelization techniques, performance tools and visualization have all played a part. Recently this technology has been applied in novel ways to research problems in mathematics and mathematical physics. In particular, high-precision numerical computations using the "PSLQ" integer relation algorithm, in many instances implemented on highly parallel computer systems, have been used to discover new mathematical formulas and identities not previously known in the literature. One notable example was the discovery a few years ago of a new formula for pi, which has the remarkable property that it permits one to directly calculate binary or hexadecimal digits beginning at an arbitrary starting position. Many other results have recently been found in this manner, particularly in the area of mathematical physics. This talk gives a brief overview of the techniques used and some of the recent results.

Biography

David H. Bailey received his B.S. in mathematics from Brigham Young University, and his Ph.D. from Stanford University. For 15 years he worked at the NAS supercomputer center at NASA's Ames Research Center, and for the last ten years at the Lawrence Berkeley Laboratory, where he is currently the Chief Technologist of the Computational Research Dept. Dr. Bailey has received the Sidney Fernbach Award from the IEEE Computer Society, and the Chauvenet and Hasse awards from the Mathematical Association of America. He has authored three books and over 100 papers in the area of computer science and mathematics.