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Hyperbolic Cross Approximation

  • Dinh Dũng
  • Vladimir Temlyakov
  • Tino Ullrich
  • Sergey Tikhonov

Part of the Advanced Courses in Mathematics - CRM Barcelona book series (ACMBIRK)

Table of contents

  1. Front Matter
    Pages i-xi
  2. Dinh Dũng, Vladimir Temlyakov, Tino Ullrich
    Pages 1-13
  3. Dinh Dũng, Vladimir Temlyakov, Tino Ullrich
    Pages 15-33
  4. Dinh Dũng, Vladimir Temlyakov, Tino Ullrich
    Pages 35-43
  5. Dinh Dũng, Vladimir Temlyakov, Tino Ullrich
    Pages 45-70
  6. Dinh Dũng, Vladimir Temlyakov, Tino Ullrich
    Pages 71-94
  7. Dinh Dũng, Vladimir Temlyakov, Tino Ullrich
    Pages 95-105
  8. Dinh Dũng, Vladimir Temlyakov, Tino Ullrich
    Pages 107-126
  9. Dinh Dũng, Vladimir Temlyakov, Tino Ullrich
    Pages 127-152
  10. Dinh Dũng, Vladimir Temlyakov, Tino Ullrich
    Pages 153-170
  11. Dinh Dũng, Vladimir Temlyakov, Tino Ullrich
    Pages 171-179
  12. Dinh Dũng, Vladimir Temlyakov, Tino Ullrich
    Pages 181-185
  13. Back Matter
    Pages 187-218

About this book

Introduction

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 their univariate counterparts, and recent findings have established that multivariate mixed smoothness classes play a fundamental role in high-dimensional approximation. The book presents essential findings on and discussions of linear and nonlinear approximations of the mixed smoothness classes. Many of the important open problems explored here will provide both students and professionals with inspirations for further research.

Keywords

hyperbolic cross sparse grid mixed smoothness trigonometric polynomial linear approximation Kolmogorov width linear width orthowidth sampling recovery sampling width nonlinear approximation entropy number best m-term approximation numerical integration cubature formulas high-dimensional approximation

Authors and affiliations

  • Dinh Dũng
    • 1
  • Vladimir Temlyakov
    • 2
  • Tino Ullrich
    • 3
  1. 1.Information Technology InstituteVietnam National UniversityHanoiVietnam
  2. 2.Department of MathematicsUniversity of South CarolinaColumbiaUSA
  3. 3.Faculty of MathematicsTechnical University of ChemnitzChemnitzGermany

Editors and affiliations

  • Sergey Tikhonov
    • 1
  1. 1.ICREA Research ProfessorCentre de Recerca MatemàticaBarcelonaSpain

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-92240-9
  • Copyright Information Springer Nature Switzerland AG 2018
  • Publisher Name Birkhäuser, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-92239-3
  • Online ISBN 978-3-319-92240-9
  • Series Print ISSN 2297-0304
  • Series Online ISSN 2297-0312
  • Buy this book on publisher's site