Greedy approximation
By: Vladimir Temlyakov
Series: Cambridge monographs on applied and computational mathematics -- 20; Cambridge monographs on applied and computational mathematics -- 20.
Publisher: Cambridge University Press
Published: 2011
Place of publication: Cambridge; New York
Language: eng
Number of pages: 418
ISBN-13: 9781107003378
Subjects: Approximation theory
Description: "This first book on greedy approximation gives a systematic presentation of the fundamental results. It also contains an introduction to two hot topics in numerical mathematics: learning theory and compressed sensing. Nonlinear approximation is becoming increasingly important, especially since two types are frequently employed in applications: adaptive methods are used in PDE solvers, while m-term approximation is used in image/signal/data processing, as well as in the design of neural networks. The fundamental question of nonlinear approximation is how to devise good constructive methods (algorithms) and recent results have established that greedy type algorithms may be the solution. The author has drawn on his own teaching experience to write a book ideally suited to graduate courses. The reader does not require a broad background to understand the material. Important open problems are included to give students and professionals alike ideas for further research"--

"An introduction to two hot topics in numerical mathematics: learning theory and compressed sensing. This book possesses features of both a survey paper and a textbook. The majority of results are given with proofs. However,some important results with technically involved proofs are presented without proof. We included proofs of the most important and typical results; and we tried to include those proofs which demonstrate different ideas and are based on different techniques. In this sense the book has a feature of a survey - it tries to cover broad material. On the other hand, we limit ourselves to a systematic treatment of a specific topic rather than trying to give an overview of all related topics. In this sense the book is close to a textbook. There are many papers on theoretical and computational aspects of greedy approximation, learning theory and compressed sensing. We have chosen to cover the mathematical foundations of greedy approximation, learning theory and compressed sensing. The book is addressed to researchers working in numerical mathematics, analysis, functional analysis and statistics. It quickly takes the reader from classical results to the frontier of the unknown, but is written at the level of a graduate course and does not require a broad background in order to understand the topics"--
Notes: Includes bibliographical references (p. 405-414) and index.
Table of contents: title: 1. Greedy approximation with respect to bases; title: 2. Greedy approximation with respect to dictionaries: Hilbert spaces; title: 3. Entropy; title: 4. Approximation in learning theory; title: 5. Approximation in compressed sensing; title: 6. Greedy approximation with respect to dictionaries: Banach spaces.