Greedy Approximation

Erscheinungsjahr 2018
ISBN: 978-1-107-00337-8
Verlag: Cambridge University Press

Buch, Englisch, Band 20, 432 Seiten, Format (B × H): 157 mm x 235 mm, Gewicht: 851 g

Reihe: Cambridge Monographs on Applied and Computational Mathematics

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.

Autoren/Hrsg.

Temlyakov, Vladimir

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen

Inhaltsverzeichnis

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.

Über Autor(innen)

Temlyakov, Vladimir
Vladimir Temlyakov is Carolina Distinguished Professor in the Department of Mathematics at the University of South Carolina.