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Approximation Theory and Algorithms for Data Analysis

  • ArminĀ Iske

Part of the Texts in Applied Mathematics book series (TAM, volume 68)

Table of contents

  1. Front Matter
    Pages I-X
  2. Armin Iske
    Pages 1-8
  3. Armin Iske
    Pages 61-102
  4. Armin Iske
    Pages 103-138
  5. Armin Iske
    Pages 139-184
  6. Armin Iske
    Pages 185-236
  7. Armin Iske
    Pages 237-273
  8. Armin Iske
    Pages 275-315
  9. Armin Iske
    Pages 317-348
  10. Back Matter
    Pages 349-358

About this book

Introduction

This textbook offers an accessible introduction to the theory and numerics of approximation methods, combining classical topics of approximation with recent advances in mathematical signal processing, and adopting a constructive approach, in which the development of numerical algorithms for data analysis plays an important role.

The following topics are covered:

* least-squares approximation and regularization methods

* interpolation by algebraic and trigonometric polynomials

* basic results on best approximations

* Euclidean approximation

* Chebyshev approximation

* asymptotic concepts: error estimates and convergence rates

* signal approximation by Fourier and wavelet methods

* kernel-based multivariate approximation

* approximation methods in computerized tomography

Providing numerous supporting examples, graphical illustrations, and carefully selected exercises, this textbook is suitable for introductory courses, seminars, and distance learning programs on approximation for undergraduate students.

Keywords

foundations approximation introduction approximation applications approximation optimization approximation examples approximation best approximation Chebychev approximation kernel-based approximation approximation methods

Authors and affiliations

  • ArminĀ Iske
    • 1
  1. 1.Department of MathematicsUniversity of HamburgHamburgGermany

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-030-05228-7
  • Copyright Information Springer Nature Switzerland AG 2018
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-030-05227-0
  • Online ISBN 978-3-030-05228-7
  • Series Print ISSN 0939-2475
  • Series Online ISSN 2196-9949
  • Buy this book on publisher's site
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