Computational methods from rational approximation theory

This special issue contains a number of papers focusing on numerical algorithms derived from the use of rational approximation methods. It is one of the three special issues of different journals that together make up the proceedings of the International Conference on Rational Approximation ICRA99, organised by Annie Cuyt and Brigitte Verdonk at the University of Antwerp (Belgium), 6–11 June 1999. This international event was held for the fourth time in Antwerp after successful meetings in 1979, 1987 and 1993. The Belgian scientific committee consisted of A. Bultheel (Leuven), A. Cuyt (Antwerpen), A. Magnus (Louvain-la-Neuve), J. Schmets (Liège), J.-P. Thiran (Namur), M. Van Barel (Leuven), P. Van Dooren (Louvain-la-Neuve) and B. Verdonk (Antwerpen). The conference focused on rational approximation theory in the broadest sense, including all computational aspects and applications. Invited as well as contributed talks were given on the subjects of Padé Approximation, Continued Fractions, Orthogonal Polynomials and Rational Approximation in general. Nonlinear numerical methods and rational approximation theory may be a narrow subject for the outside world, but from the specialists in the field more than 100 registered for participation in this conference, coming from 25 different countries. From the papers that were accepted for publication in the proceedings of ICRA99, only the ones that dealt with computational issues were published either in this volume or in a special issue of the journal Reliable Computing. The papers that discussed theoretical results or practical applications were published in a special volume of Acta Applicandae Mathematicae. The organizers would like to thank the “Fonds voor Wetenschappelijk Onderzoek – Vlaanderen”, the “Universiteit Antwerpen (UIA)” and the “Wetenschappelijke Onderzoeksgemeenschap FWO-V” for their important financial support. Thanks are also due to the technical staff of the conference centre of UIA for their know-how and impeccable service, to S. Becuwe for his involvement and almost 24-hour standby before, during and after the conference. Last but not least we want to thank the participants: you created the wonderful atmosphere that everybody could enjoy during the conference!