عنوان

Greedy approximation /

(Number (ISBN

1107003377

(Number (ISBN

9781107003378

Number

dltt

Title Proper

Greedy approximation /

General Material Designation

[Book]

First Statement of Responsibility

Vladimir Temlyakov

Specific Material Designation and Extent of Item

xiv, 418 pages :

Other Physical Details

illustrations,

Dimensions

24 cm

Series Title

Cambridge monographs on applied and computational mathematics ;

Volume Designation

20

Text of Note

Includes bibliographical references and index

Text of Note

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

8

Text of Note

"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"--

Text of Note

"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"--

Approximation theory

Number

Edition

Class number

Book number

Temlyakov, Vladimir,1953-

Date of Transaction

20111206130518.0

Cataloguing Rules (Descriptive Conventions))

rda

Electronic name

[Book]

Y