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Numerical Analysis (Second Edition) PDF

615 Pages·2012·3.47 MB·English
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Walter Gautschi Numerical Analysis Second Edition WalterGautschi DepartmentofComputerSciences PurdueUniversity 250N.UniversityStreet WestLafayette,IN47907-2066 [email protected] ISBN978-0-8176-8258-3 e-ISBN978-0-8176-8259-0 DOI10.1007/978-0-8176-8259-0 SpringerNewYorkDordrechtHeidelbergLondon LibraryofCongressControlNumber:2011941359 Mathematics Subject Classification (2010): 65-01, 65D05, 65D07, 65D10, 65D25, 65D30, 65D32, 65H04,65H05,65H10,65L04,65L05,65L06,65L10 (cid:2)c SpringerScience+BusinessMedia,LLC1997,2012 Allrightsreserved.Thisworkmaynotbetranslatedorcopiedinwholeorinpartwithoutthewritten permissionofthepublisher (Springer ScienceCBusiness Media, LLC,233SpringStreet, New York, NY10013, USA),except forbrief excerpts inconnection with reviews orscholarly analysis. Usein connectionwithanyformofinformationstorageandretrieval,electronicadaptation,computersoftware, orbysimilarordissimilarmethodologynowknownorhereafterdevelopedisforbidden. Theuseinthispublicationoftradenames,trademarks,servicemarks,andsimilarterms,eveniftheyare notidentifiedassuch,isnottobetakenasanexpressionofopinionastowhetherornottheyaresubject toproprietaryrights. Printedonacid-freepaper www.birkhauser-science.com TO E RIKA Preface to the Second Edition Inthissecondedition,theoutlineofchaptersandsectionshasbeenpreserved.The subtitle“AnIntroduction”,assuggestedbyseveralreviewers,hasbeendeleted.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 computerassignments. The typographicalappearancehasalsobeenimprovedbyprintingvectorsandmatrices consistentlyinboldfacetypes. With regardto computerlanguagein 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],HighamandHigham[2005],Hunt,LipsmanandRosenberg[2006], andDriscoll[2009],moreexclusivelyfocusedonMatlab. Themajornovelty,however,isacompletesetofdetailedsolutionstoallexercises and machine assignments. The solution manual is available to instructors upon requestatthepublisher’swebsitehttp://www.birkhauser-science.com/978-0-8176- 8258-3.Selectedsolutionsarealso includedin thetextto givestudentsanideaof whatisexpected.Thebibliographyhasbeenexpandedtoreflecttechnicaladvances in the field and to include referencesto new booksand expositoryaccounts. As a result,thetexthasundergoneanexpansioninsizeofabout20%. WestLafayette,Indiana WalterGautschi November2011 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 linearalgebra,thenumericalsolutionofordinaryandpartialdifferentialequations, and perhaps additional topics related to complex analysis, to multidimensional analysis,inparticularoptimization,andtofunctionalanalysisandrelatedfunctional equations.Viewedinthiscontext,thefirstfourchaptersofourbookcouldserveas a text for the basic introductory course, and the remaining three chapters (which indeedareatadistinctlyhigherlevel)couldprovideatextforanadvancedcourse on the numericalsolution of ordinarydifferentialequations. In a sense, therefore, the book breaks with tradition in that it does 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 differentialequations,havedevelopedintomajorfieldsofstudythathaveattained a degree of autonomy and identity that justifies their treatment in separate books and separate courses on the graduate level. The term “Numerical Analysis” as used in this book, therefore, is to be taken in the narrow sense of the numerical analogueofMathematicalAnalysis,comprisingsuchtopicsasmachinearithmetic, theapproximationoffunctions,approximatedifferentiationandintegration,andthe approximatesolutionofnonlinearequationsandofordinarydifferentialequations. What is being covered, on the other hand, is done so with a view toward stressingbasicprinciplesandmaintainingsimplicityandstudent-friendlinessasfar as possible. In this sense, the book is “An Introduction”.Topics that, even though importantandofcurrentinterest,requirealeveloftechnicalitythattranscendsthe boundsofsimplicitystrivenfor,arereferencedindetailedbibliographicnotesatthe endofeachchapter.Itishoped,inthisway,toplacethematerialtreatedinproper contextandtohelp,indeedencourage,thereadertopursueadvancedmoderntopics inmoredepth. A significant feature of the book is the large collection of exercises that are designed to help the student develop problem-solving skills and to provide interesting extensions of topics treated in the text. Particular attention is given to ix

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