Numerical Analysis (Second Edition)

615 Pages·2012·3.47 MB·English

by  Walter Gautschi

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
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TO
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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
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