Scientific Computing Vol. I - Linear and Nonlinear Equations
This is the first of three volumes providing a comprehensive presentation of the fundamentals of scientific computing. This volume discusses basic principles of computation, and fundamental numerical algorithms that will serve as basic tools for the subse
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John A. Trangenstein
Scientific Computing Vol. I – Linear and Nonlinear Equations
Editorial Board T. J.Barth M.Griebel D.E.Keyes R.M.Nieminen D.Roose T.Schlick
Texts in Computational Science and Engineering Editors Timothy J. Barth Michael Griebel David E. Keyes Risto M. Nieminen Dirk Roose Tamar Schlick
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More information about this series at http://www.springer.com/series/5151
John A. Trangenstein
Scientific Computing Vol. I – Linear and Nonlinear Equations
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John A. Trangenstein Professor Emeritus of Mathematics Department of Mathematics Duke University Durham North Carolina, USA
Additional material to this book can be downloaded from http://extras.springer.com. ISSN 1611-0994 ISSN 2197-179X (electronic) Texts in Computational Science and Engineering ISBN 978-3-319-69104-6 ISBN 978-3-319-69105-3 (eBook) https://doi.org/10.1007/978-3-319-69105-3 Library of Congress Control Number: 2018932366 Mathematics Subject Classification (2010): 15, 65 © Springer International Publishing AG, part of Springer Nature 2017 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 statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. Printed on acid-free paper This Springer imprint is published by the registered company Springer International Publishing AG part of Springer Nature. The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland
To my daughter Christina
Preface
This is the first volume in a three-volume book about scientific computing. The primary goal in these volumes is to present many of the important computational topics and algorithms used in applications such as engineering and physics, together with the theory needed to understand their proper operation. However, a secondary goal in the design of this book is to allow readers to experiment with a number of interactive programs within the book, so that readers can improve their understanding of the problems and algorithms. This
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