Approximation theory : Lecture notes prepared for the American Mathematical Society short coruse, held in New Orleans, Louisiana, January 5-6, 1986

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. Approximation Of Functions -- Polynomial And Rational Approximation In The Complex Domain -- N-widths And Optima Recovery -- Algorithms For Approximation -- Algebraic Aspects Of Interpolation -- Multivariate Splines. Carl De Boor, Editor. The Result Of The 1986 American Mathematical Society Short Course ... Given At The Annual Meeting At New Orleans, On January 5-6, 1986--pref. Includes Bibliographies And Index. Presented at a 1986 AMS Short Course, this title contains papers that give a brief introduction to approximation theory and some of its areas of active research, both theoretical and applied. It is best understood by those with a standard first graduate course in real and complex analysis.