Scientific Computing with MATLAB and Octave

TextsinComputationalScienceandEngineering2EditorsTimothyJ.BarthMichaelGriebelDavidE.KeyesRistoM.NieminenDirkRooseTamarSchlickAlfioQuarteroniFaustoSaleriScientificComputingwithMATLABandOctaveSecondEditionWith108Figuresand12TablesABCAlfioQuarteroniEcolePolytechniqueFédéraledeLausanneCMCS-ModelingandScientificComputing1015Lausanne,SwitzerlandandMOX-PolitecnicodiMilanoPiazzaLeonardodaVinci3220133Milano,ItalyE-mail:alfio.quarteroni@epfl.chFaustoSaleriMOX-PolitecnicodiMilanoPiazzaLeonardodaVinci3220133Milano,ItalyE-mail:[e-mail]figurebyMarzioSalaTitleoftheItalianoriginaledition:IntroduzionealCalcoloScientifico,Springer-VerlagItalia,Milano,2006,ISBN88-470-0480-2LibraryofCongressControlNumber:2006928277MathematicsSubjectClassification:65-01,68U01,68N15ISBN-103-540-32612-XSpringerBerlinHeidelbergNewYorkISBN-13978-3-540-32612-0SpringerBerlinHeidelbergNewYorkISBN-103-540-44363-01stEditionSpringerBerlinHeidelbergNewYorkThisworkissubjecttocopyright.Allrightsarereserved,whetherthewholeorpartofthematerialisconcerned,specificallytherightsoftranslation,reprinting,reuseofillustrations,recitation,broadcasting,reproductiononmicrofilmorinanyotherway,andstorageindatabanks.DuplicationofthispublicationorpartsthereofispermittedonlyundertheprovisionsoftheGermanCopyrightLawofSeptember9,1965,initscurrentversion,andpermissionforusemustalwaysbeobtainedfromSpringer.ViolationsareliableforprosecutionundertheGermanCopyrightLaw.SpringerisapartofSpringerScience+BusinessMediaspringer.comc
Springer-VerlagBerlinHeidelberg2003,2006PrintedinTheNetherlandsTheuseofgeneraldescriptivenames,registerednames,trademarks,etc.inthispublicationdoesnotimply,evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfromtherelevantprotectivelawsandregulationsandthereforefreeforgeneraluse.Typesetting:bytheauthorsandtechbooksusingaSpringerLATEXmacropackageCoverdesign:design&productionGmbH,HeidelbergPrintedonacid-freepaperSPIN:1167879346/techbooks543210ThisbookisdedicatedtoFulvia,SilviaandMarzia,Paola,MariaandCaterina,whomakeourliveslessscientificallycomputed.PrefacePrefacetotheFirstEditionThistextbookisanintroductiontoScientificComputing.Wewillillustrateseveralnumericalmethodsforthecomputersolutionofcer-tainclassesofmathematicalproblemsthatcannotbefacedbypaperandpencil.Wewillshowhowtocomputethezerosortheintegralsofcontinuousfunctions,solvelinearsystems,approximatefunctionsbypolynomialsandconstructaccurateapproximationsforthesolutionofdifferentialequations.Withthisaim,inChapter1wewillillustratetherulesofthegamethatcomputersadoptwhenstoringandoperatingwithrealandcomplexnumbers,vectorsandmatrices.InordertomakeourpresentationconcreteandappealingwewilladopttheprogrammingenvironmentMATLAB
1asafaithfulcom-panion.Wewillgraduallydiscoveritsprincipalcommands,statementsandconstructs.Wewillshowhowtoexecuteallthealgorithmsthatweintroducethroughoutthebook.Thiswillenableustofurnishanim-mediatequantitativeassessmentoftheirtheoreticalpropertiessuchasstability,accuracyandcomplexity.Wewillsolveseveralproblemsthatwillberaisedthroughexercisesandexamples,oftenstemmingfromspe-cificapplications.Severalgraphicaldeviceswillbeadoptedinordertorendertheread-ingmorepleasant.WewillreportinthemargintheMATLABcommandalongsidethelinewherethatcommandisbeingintroducedforthefirsttime.Thesymbolwillbeusedtoindicatethepresenceofexercises,thesymboltoindicatethepresenceofaMATLABprogram,while1MATLABisatrademarkofTheMathWorksInc.,24PrimeParkWay,Nat-ick,MA01760,Tel:001+508-647-7000,Fax:001+508-647-7001.VIIIPrefacethesymbolwillbeusedwhenwewanttoattracttheattentionofthereaderonacriticalorsurprisingbehaviorofanalgorithmorapro-cedure.Themathematicalformulaeofspecialrelevanceareputwithinaframe.Finally,thesymbolindicatesthepresenceofadisplaypanelsummarizingconceptsandconclusionswhichhavejustbeenreportedanddrawn.Attheendofeachchapteraspecificsectionisdevotedtomentioningthosesubjectswhichhavenotbeenaddressedandindicatethebiblio-graphicalreferencesforamorecomprehensivetreatmentofthematerialthatwehavecarriedout.Quiteoftenwewillrefertothetextbook[QSS06]wheremanyissuesfacedinthisbookaretreatedatadeeperlevel,andwheretheoreticalre-sultsareproven.ForamorethoroughdescriptionofMATLABwereferto[HH05].Alltheprogramsintroducedinthistextcanbedownloadedfromthewebaddressmox.polimi.it/qsNospecialprerequisiteisdemandedofthereader,withtheexceptionofanelementarycourseofCalculus.However,inthecourseofthefirstchapter,werecalltheprincipalre-sultsofCalculusandGeometrythatwillbeusedextensivelythroughoutthistext.Thelesselementarysubjects,thosewhicharenotsoneces-saryforanintroductoryeducationalpath,arehighlightedbythespecialsymbol.WeexpressourthankstoThanh-HaLeThifromSpringer-VerlagHeidelberg,andtoFrancescaBonadeiandMarinaForlizzifromSpringer-Italiafortheirfriendlycollaborationthroughoutthisproject.Wegrate-fullythankProf.EasthamofCardiffUniversityforeditingthelanguageofthewholemanuscriptandstimulatingustoclarifymanypointsofourtext.MilanoandLausanneAlfioQuarteroniMay2003FaustoSaleriPrefacetotheSecondEditionInthissecondeditionwehaveenrichedallth