 CARMA ANALYSIS AND NUMBER THEORY SEMINAR
 Speaker: Prof David Bailey, Berkeley, California
 Title: HighPrecision Numerical Integration and Experimental Mathematics
 Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle
 Time and Date: 3:30 pm, Wed, 18^{th} Aug 2010
 Abstract:
Computation of definite integrals to high precision (typically several hundred digit precision) has emerged as a particularly fruitful tool for experimental mathematics. In many cases, integrals with no known analytic evaluations have been experimentally evaluated (pending subsequent formal proof) by applying techniques such as the PSLQ integer relation algorithm to the output numerical values. In other cases, intriguing linear relations have been found in a class of related integrals, relations which have subsequently been proven as instances of more general results. In this lecture, Bailey will introduce the two principal algorithms used for highprecision integration, namely Gaussian quadrature and tanhsinh quadrature, with some details on efficient computer implementations. He will also present numerous examples of new mathematical results obtained, in part, by using these methods. In a subsequent lecture, Bailey will discuss the PSLQ algorithm and give the details of efficient multilevel and parallel implementations.
 Download: Seminar slides
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