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1、RadialBasisFunctions:TheoryandImplementationsM.D.BUHMANNUniversityofGiessenpublishedbythepresssyndicateoftheuniversityofcambridgeThePittBuilding,TrumpingtonStreet,Cambridge,UnitedKingdomcambridgeuniversitypressTheEdinburghBuilding,CambridgeCB22RU,UK40West20thStreet,N
2、ewYork,NY10011-4211,USA477WilliamstownRoad,PortMelbourne,VIC3207,AustraliaRuizdeAlarc´on13,28014Madrid,SpainDockHouse,TheWaterfront,CapeTown8001,SouthAfricahttp://www.cambridge.orgCCambridgeUniversityPress2003Thisbookisincopyright.Subjecttostatutoryexceptionandtothe
3、provisionsofrelevantcollectivelicensingagreements,noreproductionofanypartmaytakeplacewithoutthewrittenpermissionofCambridgeUniversityPress.Firstpublished2003PrintedintheUnitedKingdomattheUniversityPress,CambridgeTypefaceTimes10/13ptSystemLATEX2ε[tb]Acataloguerecordfo
4、rthisbookisavailablefromtheBritishLibraryLibraryofCongressCataloguinginPublicationdataBuhmann,M.D.(MartinDietrich),1963–Radialbasisfunctions:theoryandimplementations/MartinBuhmann.p.cm.–(Cambridgemonographsonappliedandcomputationalmathematics;12)Includesbibliographic
5、alreferencesandindex.ISBN05216333891.Radialbasisfunctions.I.Title.II.Series.QA223.B842003511.42–dc212002034983ISBN0521633389hardbackContentsPrefacepageix1Introduction11.1Radialbasisfunctions21.2Applications51.3Contentsofthebook82Summaryofmethodsandapplications112.1I
6、nvertibilityofinterpolationmatrices112.2Convergenceanalysis162.3Interpolationandconvergence232.4ApplicationstoPDEs293Generalmethodsforapproximationandinterpolation363.1Polynomialschemes373.2Piecewisepolynomials413.3Generalnonpolynomialmethods454Radialbasisfunctionapp
7、roximationoninfinitegrids484.1Existenceofinterpolants494.2Convergenceanalysis654.3Numericalpropertiesoftheinterpolationlinearsystem894.4Convergencewithrespecttoparametersintheradialfunctions955Radialbasisfunctionsonscattereddata995.1Nonsingularityofinterpolationmatric
8、es1005.2Convergenceanalysis1055.3Normestimatesandconditionnumbersofinterpolationmatrices136viiviiiContents6Radialbasisfunctionswith
