Approximation Theory and Algorithms for Data Analysis

 
 
Springer (Verlag)
  • erschienen am 3. Januar 2019
 
  • Buch
  • |
  • Hardcover
  • |
  • X, 358 Seiten
978-3-030-05227-0 (ISBN)
 
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.
Book
1st ed. 2018
  • Englisch
  • Cham
  • |
  • Schweiz
Springer International Publishing
  • Für höhere Schule und Studium
  • 20 farbige Tabellen, 15 farbige Abbildungen, 19 s/w Abbildungen
  • |
  • 18 schwarz-weiße und 15 farbige Abbildungen, 20 farbige Tabellen, Bibliographie
  • Höhe: 241 mm
  • |
  • Breite: 163 mm
  • |
  • Dicke: 30 mm
  • 741 gr
978-3-030-05227-0 (9783030052270)
10.1007/978-3-030-05228-7
weitere Ausgaben werden ermittelt
Armin Iske is professor of numerical approximation at the Department of Mathematics of the University of Hamburg.
1 Introduction.- 2 Basic Methods and Numerical Analysis.- 3 Best Approximations.- 4 Euclidean Approximations.- 5 Chebyshev Approximations.- 6 Asymptotic Results.- 7 Basic Concepts of Signal Approximation.- 8 Kernel-Based Approximation.- 9 Computational Topology.- References.- Subject Index.- Name Index.
"This book is an excellent first course in approximation theory, covering all the aspects from theoretical results to practical methods, from discrete to continuous approximation, from univariate to multivariate. ... The book is an excellent text for an undergraduate course in approximation methods. ... this book is a very important textbook on approximation theory and its methods." (Ana Cristina Matos, Mathematical Reviews, August, 2019)
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.
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