About this Title
Carl de Boor, Editor
Publication: Proceedings of Symposia in Applied Mathematics
Publication Year: 1986; Volume 36
ISBNs: 978-0-8218-0098-0 (print); 978-0-8218-9251-0 (online)
The papers in this book, first presented at a 1986 AMS Short Course, give a brief introduction to approximation theory and some of its current areas of active research, both theoretical and applied. The first lecture describes and illustrates the basic concerns of the field. Topics highlighted in the other lectures include the following: approximation in the complex domain, $N$-width, optimal recovery, interpolation, algorithms for approximation, and splines, with a strong emphasis on a multivariate setting for the last three topics.
The book is aimed at mathematicians interested in an introduction to areas of current research and to engineers and scientists interested in exploring the field for possible applications to their own fields. The book is best understood by those with a standard first graduate course in real and complex analysis, but some of the presentations are accessible with the minimal requirements of advanced calculus and linear algebra.
Table of Contents
- Ronald A. DeVore – Approximation of functions [MR 864363]
- E. B. Saff – Polynomial and rational approximation in the complex domain [MR 864364]
- A. Pinkus – $n$-widths and optimal recovery [MR 864365]
- E. W. Cheney – Algorithms for approximation [MR 864366]
- Charles A. Micchelli – Algebraic aspects of interpolation [MR 864367]
- Klaus Höllig – Multivariate splines [MR 864368]