Effective Bounds in Euler-Maclaurin-Based Quadrature

Jonathan M. Borwein Faculty of Computer Science Dalhousie University Halifax, NS

DEPARTMENT SEMINAR DATE: Friday, May 26, 2006 TIME: 3:00pm PLACE: Thorvaldson 159 *** Everyone is welcome ***

Abstract

We analyze the behavior of Euler-Maclaurin-based integration schemes with the intention of deriving accurate and economic estimations of the error. These schemes typically provide very high-precision results (hundreds or thousands of digits), in reasonable run time, even in cases where the integrand function has a blow-up singularity or infinite derivative at an endpoint. Heretofore, researchers using these schemes have relied mostly on ad hoc error estimation schemes to project the estimated error of the present iteration. In this talk, we describe some more rigorous, yet highly usable schemes to estimate these errors.

About the speaker

Jonathan M. Borwein was Shrum Professor of Science (1993-2003) and a Canada Research Chair in Information Technology (2001-08) at Simon Fraser University, and was founding Director of the Centre for Experimental and Constructive Mathematics. In 2004, he (re-)joined the Faculty of Computer Science at Dalhousie as a Canada Research Chair in Distributed and Collaborative Research, cross-appointed in Mathematics, with an adjunct appointment at Simon Fraser. He was born in St Andrews in 1951, and received his D.Phil. from Oxford in 1974, as a Rhodes Scholar. Prior to joining SFU in 1993, he worked at Dalhousie (1974-91), Carnegie-Mellon (1980-82) and Waterloo (1991-93).

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