Numerical Methods Based on Sinc and Analytic Functions
Many mathematicians, scientists, and engineers are familiar with the Fast Fourier Transform, a method based upon the Discrete Fourier Transform. Perhaps not so many mathematicians, scientists, and engineers recognize that the Discrete Fourier Transform is
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Editorial Board R.L. Graham, Murray Hill (NJ) J. Stoer, Wurzburg R. Varga, Kent (Ohio)
Frank Stenger
Numerical Methods Based on Sinc and Analytic Functions
Springer-Verlag New York Berlin Heidelberg London Paris Tokyo Hong Kong Barcelona Budapest
Frank Stenger Department of Computer Science The University of Utah Salt Lake City, UT 84112 USA
Mathematics Subject Classification: 30-00; 65-00
With 8 Illustrations.
Library of Congress Cataloging-in-Publication Data Stenger, Frank. Numerical methods based on Sinc and analytic functions/Frank Stenger. p. cm. - (Springer series in computational mathematics; 20) Includes bibliographical references and index. ISBN-13:978-1-4612-7637-1 1. Galerkin methods. 2. Differential equations-Numerical solutions. I. Title. II. Series. QA372.S82 1993 515' .352-dc20 93-9403 Printed on acid-free paper.
© 1993 Springer-Verlag New York, Inc. Softcover reprint of the hardcover 1st edition 1993 All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Springer-Verlag New York, Inc., 175 Fifth Avenue, New York, NY 10010, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use of general descriptive names, trade names, trademarks, etc., in this publication, even if the former are not especially identified, is not to be taken as a sign that such names, as understood by the Trade Marks and Merchandise Marks Act, may accordingly. be used freely by anyone. Production managed by Natalie Johnson; manufacturing supervised by Vincent Scelta. Photocomposed copy prepared from the author's LaTEX file. 987654321
ISBN-13:978-1-4612-7637-1 e-ISBN-13: 978-1-4612-2706-9 DOl: 10.1007/978-1-4612-2706-9
Preface The primary purpose of this text is to familiarize the student and computational scientist with the use of Sine methods. These methods fill a void in computational mathematics in a manner similar to the way in which polynomials, splines, and Fourier polynomials fill a void; although we can get by without the methods based on these functions, our environment is made richer when the methods are available. Indeed, once one gets accustomed to using the methods in anyone of these classes, it is difficult to get along without them. Each existing method excels in some particular class of problems. For example, polynomials excel in the approximation of analytic functions without singularities, splines are particularly good for approximating measured, or noisy data, while Fourier polynomials excel in the approximation of functions that are both smooth and periodic over the whole real line. Sinc methods excel for problems with singularities, for boundary-layer problems and for problems over infinite or semi-infinite ranges. The error of rational function approximation is the same as the error of Si
