This monograph discusses the qualitative linear theory of best L DEGREEST1-approximation from finite-dimensional subspaces. It presents a survey of recent research that extends "classical" results concerned with best-uniform approximation to the more general case. The work is organized to serve as a self-study guide or as a text for advanced courses. It begins with a basic introduction to the concepts of approximation theory before addressing 1- or 2-sided best approximations from finite-dimensional subspaces and approaches to the computation of these. At the end of each chapter is a series...

This volume provides a basic understanding of Fourier series, Fourier transforms, and Laplace transforms. It is an expanded and polished version of the authors' notes for a one-semester course intended for students of mathematics, electrical engineering, physics and computer science. Prerequisites for readers of this book are a basic course in both calculus and linear algebra. The material is self contained with numerous exercises and various examples of applications.

This volume is a collection of articles based on the plenary talks presented at the 2005 meeting in Santander of the Society for the Foundations of Computational Mathematics. The talks were given by some of the foremost world authorities in computational mathematics. The topics covered reflect the breadth of research within the area as well as the richness and fertility of interactions between seemingly unrelated branches of pure and applied mathematics. As a result this volume will be of interest to researchers in the field of computational mathematics and also to non-experts who wish to...

This volume provides a basic understanding of Fourier series, Fourier transforms, and Laplace transforms. It is an expanded and polished version of the authors' notes for a one-semester course intended for students of mathematics, electrical engineering, physics and computer science. Prerequisites for readers of this book are a basic course in both calculus and linear algebra. The material is self contained with numerous exercises and various examples of applications.

Surveys and summaries of the latest research in numerical analysis, optimization, computer algebra and scientific computing.

Totally positive matrices constitute a particular class of matrices, the study of which was initiated by analysts because of its many applications in diverse areas. This account of the subject is comprehensive and thorough, with careful treatment of the central properties of totally positive matrices, full proofs and a complete bibliography. The history of the subject is also described: in particular, the book ends with a tribute to the four people who have made the most notable contributions to the history of total positivity: I. J. Schoenberg, M. G. Krein, F. R. Gantmacher and S. Karlin....

Presents the state of the art in the theory of ridge functions, providing a solid theoretical foundation.