- Clear and comprehensible introduction to approximation theory and its applications
- Offers a constructive approach to methods and algorithms
- Contains a large number of examples and exercises
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- About this Textbook
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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.
- About the authors
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Armin Iske is professor of numerical approximation at the Department of Mathematics of the University of Hamburg.
- Reviews
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“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)
- Table of contents (9 chapters)
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Introduction
Pages 1-8
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Basic Methods and Numerical Algorithms
Pages 9-59
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Best Approximations
Pages 61-102
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Euclidean Approximation
Pages 103-138
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Chebyshev Approximation
Pages 139-184
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Table of contents (9 chapters)
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Bibliographic Information
- Bibliographic Information
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- Book Title
- Approximation Theory and Algorithms for Data Analysis
- Authors
-
- Armin Iske
- Series Title
- Texts in Applied Mathematics
- Series Volume
- 68
- Copyright
- 2018
- Publisher
- Springer International Publishing
- Copyright Holder
- Springer Nature Switzerland AG
- eBook ISBN
- 978-3-030-05228-7
- DOI
- 10.1007/978-3-030-05228-7
- Hardcover ISBN
- 978-3-030-05227-0
- Series ISSN
- 0939-2475
- Edition Number
- 1
- Number of Pages
- X, 358
- Number of Illustrations
- 19 b/w illustrations, 15 illustrations in colour
- Additional Information
- Original German edition published by Springer-Verlag GmbH, Heidelberg, 2017. Title of German edition: Approximation.
- Topics
