Includes bibliographical references and index.

Machine generated contents note: Preface; 1. Greedy approximation with respect to bases; 2. Greedy approximation with respect to dictionaries: Hilbert spaces; 3. The entropy; 4. Approximation in learning theory; 5. Approximation in compressed sensing; 6. Greedy approximation with respect to dictionaries: Banach spaces; References; Index.

"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"-- Provided by publisher.

Electronic reproduction. Palo Alto, Calif. : ebrary, 2013. Available via World Wide Web. Access may be limited to ebrary affiliated libraries.