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Walter Gautschi

Numerical Analysis

Second Edition

Walter Gautschi

Department of Computer Sciences

Purdue University

250 N. University Street

West Lafayette, IN 47907-2066

wgautschi@purdue.edu

ISBN 978-0-8176-8258-3 e-ISBN 978-0-8176-8259-0

DOI 10.1007/978-0-8176-8259-0

Springer New York Dordrecht Heidelberg London

Library of Congress Control Number: 2011941359

Mathematics Subject Classification (2010): 65-01, 65D05, 65D07, 65D10, 65D25, 65D30, 65D32,

65H04, 65H05, 65H10, 65L04, 65L05, 65L06, 65L10

c ?Springer Science+Business Media, LLC 1997, 2012

All rights reserved. This work may not be translated or copied in whole or in part without the written

permission of the publisher (Springer ScienceCBusiness Media, LLC, 233 Spring Street, New York, NY 10013, 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 nowknown or hereafter developed is forbidden.

The use in this publication of trade names, trademarks, service marks, and similar terms, even if they are

not identified as such, is not to be taken as an expression of opinion as to whether or not they are subject

to proprietary rights.

Printed on acid-free paper

www.birkhauser-science.com TO ERIKA

Preface to the Second Edition

In this second edition, the outline of chapters and sections has been preserved. The subtitle ÒAn IntroductionÓ,as suggested by several reviewers, has been deleted. The content, however, is brought up to date, both in the text and in the notes. Many passages in the text have been either corrected or improved. Some biographical notes have been added as well as a few exercises and computer assignments. The typographical appearance has also been improved by printing vectors and matrices consistently in boldface types. With regard to computer language in illustrations and exercises, we now adopt uniformly Matlab. For readers not familiar with Matlab, there are a number of introductory texts available, some, like Moler [2004], Otto and Denier [2005], Stanoyevitch [2005] that combine Matlab with numerical computing, others, like Knight [2000], Higham and Higham [2005], Hunt, Lipsman and Rosenberg [2006], and Driscoll [2009], more exclusively focused on Matlab. Themajornovelty,however,is acompleteset ofdetailedsolutionstoallexercises and machine assignments. The solution manual is available to instructors upon request at the publisherÕs websitehttp://www.birkhauser-science.com/978-0-8176-

8258-3

. Selected solutions are also included in the text to give students an idea of what is expected. The bibliographyhas been expanded to reßect technical advances in the Þeld and to include references to new books and expository accounts. As a result, the text has undergone an expansion in size of about 20%.

West Lafayette, Indiana Walter Gautschi

November 2011

vii

Preface to the First Edition

The book is designed for use in a graduate program in Numerical Analysis that is structured so as to include a basic introductory course and subsequent more specialized courses. The latter are envisaged to cover such topics as numerical linear algebra, the numerical solution of ordinary and partial differential equations, and perhaps additional topics related to complex analysis, to multidimensional analysis, in particularoptimization,and to functionalanalysis and related functional equations. Viewed in this context, the Þrst four chapters of our book could serve as a text for the basic introductory course, and the remaining three chapters (which indeed are at a distinctly higher level) could provide a text for an advanced course on the numerical solution of ordinary differential equations. In a sense, therefore, the book breaks with tradition in that itdoes no longer attempt to deal with all major topics of numerical mathematics. It is felt by the author that some of the current subdisciplines, particularly those dealing with linear algebra and partial differential equations, have developed into major Þelds of study that have attained a degree of autonomy and identity that justiÞes their treatment in separate books and separate courses on the graduate level. The term ÒNumerical AnalysisÓ as used in this book, therefore, is to be taken in the narrow sense of the numerical analogue of Mathematical Analysis, comprising such topics as machine arithmetic,quotesdbs_dbs7.pdfusesText_5