Hyperbolic Cross Approximation

• Main Authors: Dũng, Dinh (Author, http://id.loc.gov/vocabulary/relators/aut), Temlyakov, Vladimir (http://id.loc.gov/vocabulary/relators/aut), Ullrich, Tino (http://id.loc.gov/vocabulary/relators/aut)
• Corporate Author: SpringerLink (Online service)
• Other Authors: Tikhonov, Sergey (Editor, http://id.loc.gov/vocabulary/relators/edt)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Birkhäuser, 2018.
• Edition: 1st ed. 2018.
• Series: Advanced Courses in Mathematics - CRM Barcelona,
• Subjects: Approximation theory.; Numerical analysis.; Approximations and Expansions.; Numerical Analysis.

This book provides a systematic survey of classical and recent results on hyperbolic cross approximation. Motivated by numerous applications, the last two decades have seen great success in studying multivariate approximation. Multivariate problems have proven to be considerably more difficult than...

Table of Contents:

• Introduction
• Trigonometric polynomials
• Function spaces on T^d
• Linear approximation
• Sampling recovery
• Entropy numbers
• Best m-term approximation
• Numerical integration
• Related problems
• High-dimensional approximation
• Appendix.