Fighting Gibbs Phenomenon by Quotienting
Staff - Faculty of Informatics
Start date: 20 April 2010
End date: 21 April 2010
The Faculty of Informatics is pleased to announce a seminar given by Jean-Paul Berrut
DATE: Tuesday, April 20th, 2010
PLACE: USI Università della Svizzera italiana, room SI-008, Informatics building (Via G. Buffi 13)
Gibbs' phenomenon, the overshooting at jumps, is a very annoying drawback of infinitely smooth approximants. Many methods for its alleviation have been suggested, in the past as well as and in recent years, see, e.g., the book by Jerri and the articles by Gottlieb, Gelb, Brezinski, Beckermann and their coauthors. Many of these methods do not act in physical space, but rather in a transformed space.
A very simple method working in physical space seems to have been overlooked so far. It is based on the following observation: for a given approximation operator, the quotient of the approximant and the approximated function f is very similar for various f. In this talk I shall present some conjectures precizing this observation and demonstrate how it may be used to alleviate, and in many cases even eliminate, the phenomenon. I also elaborate on a connection between the quotiented sinc interpolant and barycentric rational interpolation, in particular with the Floater and Hormann weights.
Jean-Paul Berrut performed his university studies in Zurich, receiving a PhD from the ETH, where he was Peter Henrici's last official student, and a lic. oec. publ. from the University. After having taught one year at the University of North Carolina in Chapel Hill and two years at the University of California in San Diego, he became a professor of numerical analysis at the University of Fribourg in 1988.
HOST: Prof. Kai Hormann