Approximation Theory and Algorithms for Data Analysis

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 dev

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Armin Iske

Approximation Theory and Algorithms for Data Analysis

Texts in Applied Mathematics Volume 68

Editors-in-chief S. S. Antman, University of Maryland, College Park, USA A. Bloch, University of Michigan, Public University, City of Michigan, USA A. Goriely, Universiyty of Oxford, Oxford, UK L. Greengard, New York University, New York, USA P. J. Holmes, Princeton University, Princeton, USA Series editors J. Bell, Lawrence Berkeley National Lab, Berkeley, USA R. Kohn, New York University, New York, USA P. Newton, University of Southern California, Los Angeles, USA C. Peskin, New York University, New York, USA R. Pego, Carnegie Mellon University, Pittsburgh, USA L. Ryzhik, Stanford University, Stanford, USA A. Singer, Princeton University, Princeton, USA A. Stevens, Max-Planck-Institute for Mathematics, Leipzig, Germany A. Stuart, University of Warwick, Coventry, UK T. Witelski, Duke University, Durham, USA S. Wright, University of Wisconsin, Madison, USA

The mathematization of all sciences, the fading of traditional scientific boundaries, the impact of computer technology, the growing importance of computer modeling and the necessity of scientific planning all create the need both in education and research for books that are introductory to and abreast of these developments. The aim of this series is to provide such textbooks in applied mathematics for the student scientist. Books should be well illustrated and have clear exposition and sound pedagogy. Large number of examples and exercises at varying levels are recommended. TAM publishes textbooks suitable for advanced undergraduate and beginning graduate courses, and complements the Applied Mathematical Sciences (AMS) series, which focuses on advanced textbooks and research-level monographs.

More information about this series at http://www.springer.com/series/1214

Armin Iske

Approximation Theory and Algorithms for Data Analysis

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Armin Iske Department of Mathematics University of Hamburg Hamburg, Germany

ISSN 0939-2475 ISSN 2196-9949 (electronic) Texts in Applied Mathematics ISBN 978-3-030-05227-0 ISBN 978-3-030-05228-7 (eBook) https://doi.org/10.1007/978-3-030-05228-7 Library of Congress Control Number: 2018963282 Mathematics Subject Classification (2010): 41-XX, 42-XX, 65-XX, 94A12 Original German edition published by Springer-Verlag GmbH, Heidelberg, 2017. Title of German edition: Approximation. © Springer Nature Switzerland AG 2018 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific stat