Best uniform polynomial approximation to 1/x

Description

Many years ago, dealing with special functions was a tedious, time-consuming, and errorprone task, which required long training, skillful manipulations and structural insight. This is now mostly obsolete: today there is an increasing number of symbolic algorithms available which are capable of dealing with special functions~\cite{AAR}. In particular, questions about orthogonal polynomials which often arise in numerical mathematics can be answered by packages for holonomic functions. With these programs, dealing with special functions is straight-forward, fast, and reliable. Recently we used an algorithm developed by Manuel Kauers~\cite{MK} for deriving a three term recurrence for the polynomial of best uniform approximation to $1/x$ on a finite interval~\cite{JM,Rivlin}. This recurrence relation entered the analysis of an algebraic multilevel iteration method. We will give an introduction to the underlying symbolic algorithm and its scope, and sketch our application to algebraic multigrid methods.

Period	06 Jul 2010
Event title	I Jaen Conference on Approximation, Ubeda
Event type	Conference
Location	SpainShow on map