Approximation techniques for engineers PDF
Preview Approximation techniques for engineers
APPROXIMATION TECHNIQUES for ENGINEERS APPROXIMATION TECHNIQUES FOR ENGINEERS Louis Komzsik UGS Corp. Cypress, California Boca Raton London New York CRC is an imprint of the Taylor & Francis Group, an informa business CRC Press Taylor & Francis Group 6000 Broken Sound Parkway NW, Suite 300 Boca Raton, FL 33487-2742 © 2007 by Taylor & Francis Group, LLC CRC Press is an imprint of Taylor & Francis Group, an Informa business No claim to original U.S. Government works Printed in the United States of America on acid-free paper 10 9 8 7 6 5 4 3 2 1 International Standard Book Number-10: 0-8493-9277-2 (Hardcover) International Standard Book Number-13: 978-0-8493-9277-1 (Hardcover) This book contains information obtained from authentic and highly regarded sources. Reprinted material is quoted with permission, and sources are indicated. A wide variety of references are listed. Reasonable efforts have been made to publish reliable data and information, but the author and the publisher cannot assume responsibility for the validity of all materials or for the conse- quences of their use. No part of this book may be reprinted, reproduced, transmitted, or utilized in any form by any electronic, mechanical, or other means, now known or hereafter invented, including photocopying, microfilming, and recording, or in any information storage or retrieval system, without written permission from the publishers. For permission to photocopy or use material electronically from this work, please access www. copyright.com (http://www.copyright.com/) or contact the Copyright Clearance Center, Inc. (CCC) 222 Rosewood Drive, Danvers, MA 01923, 978-750-8400. CCC is a not-for-profit organization that provides licenses and registration for a variety of users. For organizations that have been granted a photocopy license by the CCC, a separate system of payment has been arranged. Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation without intent to infringe. Visit the Taylor & Francis Web site at http://www.taylorandfrancis.com and the CRC Press Web site at http://www.crcpress.com T&F_LOC_A_Master.indd 1 6/14/06 9:32:47 AM To my wife, Gabriella Preface This book is a collection of methods that provide an approximate result for certain engineering computations. The di(cid:11)erence from the analytical result (if such exists at all) occurs due to the formulation chosen to execute a com- putation. As such, it must be distinguished from numerical errors occurring due to the computational round-o(cid:11)errorof the (cid:12)nite precision of computers. Thereisaperennialquestbymathematiciansandengineersto(cid:12)ndapprox- imate results in two classes of problems. In one class, the input data may only be given by a discrete set of points to describe the continuous geometry of a physical phenomenon; however, a continuous function (cid:12)tting the data is sought. Itisalsopossibleinthisclassthattheinputdataisgivenbyfunctions thatneedtobeapproximatedbyanotherfunctionorsomediscretequantities ofthefunctions(suchasderivativeatcertainpoint)arerequired. Intheother class, usually a continuous problem is posed and an approximate solution at a discrete set of points is desired, forpracticalreasonssuch as computational cost. Accordingly, the book is divided into two parts: data approximation tech- niques and approximate solutions. The (cid:12)rst part starts with the classical interpolation methods, followed by spline interpolations and least square ap- proximations. It also covers various approximations of functions as well as their numerical di(cid:11)erentiation and integration. The second part ranges from the solution of algebraic equations, linear and nonlinear systems, through eigenvalue problems to initial and boundary value problems. Both parts em- phasize the logical thread and common principles of the approximationtech- niques. The book is intended to be an everyday tool as a reference book for prac- ticing engineers, researchers and graduate engineering students. It is hoped thatthe readerscansolveaparticularapproximationproblemarisingintheir practice by directly focusing on a chapter or section describing the appropri- ate techniques. Louis Komzsik vii Acknowledgments Iwouldliketothankmycoworker,Dr.LeonardHo(cid:11)nungofUGS forhiscare- fulmathematicalproofreadingandveri(cid:12)cationofthecomputationalexamples whilerepresentingasoftwareengineer’sperspective. Ialsoappreciatethecom- mentsandrecommendationsofDr.JonathanHartofNorthrop-GrummanCor- poration, whoalso veri(cid:12)edthe mathematical details andreadthe manuscript with the eye of the application engineer. Manythanksareduetothegreatsta(cid:11)ofTaylorandFrancisBooks. Specif- ically, I would like to acknowledge the most enthusiastic support from Nora Konopka, publisher and Helena Redshaw, manager. I am grateful for very valuable corrections and contributions from Gloria Goss, proofreader and Michael Davidson, editor. Louis Komzsik ThemodelinthecoverartisbycourtesyofDaimlerChryslerCorporation. The rendering is intended to illustrate the wide-spread use of approximation techniques. The engineering audience and the engineering applications are represented by the car model. In addition, biological and environmental sci- ences, depicted by the human and the road models, also frequently use the approximation techniques of this book. ix
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