Convergence Estimates in Approximation Theory
The study of linear positive operators is an area of mathematical studies with significant relevance to studies of computer-aided geometric design, numerical analysis, and differential equations. This book focuses on the convergence of linear positive ope
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nvergence Estimates in Approximation Theory
Convergence Estimates in Approximation Theory
Vijay Gupta • Ravi P. Agarwal
Convergence Estimates in Approximation Theory
123
Vijay Gupta School of Applied Sciences Netaji Subhas Institute of Technology New Delhi, India
Ravi P. Agarwal Department of Mathematics Texas A&M University - Kingsville Kingsville, TX, USA
ISBN 978-3-319-02764-7 ISBN 978-3-319-02765-4 (eBook) DOI 10.1007/978-3-319-02765-4 Springer Cham Heidelberg New York Dordrecht London Library of Congress Control Number: 2013956134 Mathematics Subject Classification (2010): 41A36, 41A25, 41A17, 30E10 © Springer International Publishing Switzerland 2014 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. Exempted from this legal reservation are brief excerpts in connection with reviews or scholarly analysis or material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. Duplication of this publication or parts thereof is permitted only under the provisions of the Copyright Law of the Publisher’s location, in its current version, and permission for use must always be obtained from Springer. Permissions for use may be obtained through RightsLink at the Copyright Clearance Center. Violations are liable to prosecution under the respective Copyright Law. 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 statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. While the advice and information in this book are believed to be true and accurate at the date of publication, neither the authors nor the editors nor the publisher can accept any legal responsibility for any errors or omissions that may be made. The publisher makes no warranty, express or implied, with respect to the material contained herein. Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)
Preface
The aim of the general approximation methods concerning linear positive operators is to deal with convergence behavior. The accuracy can be ascertained to a desired degree by applying different methods. We are also concerned with the amount of computation required to achieve this accuracy. A direct theorem provides the order of approximation for functions of specified smoothness. The converse of the direct result, that is, the inverse theorem, infers the nature of smoothness of the function from its order of approximation. Asymptotic analysis is a
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