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1、PRODUCTSSOLUTIONSPURCHASESUPPORTCOMPANYOURSITESDOCUMENTATIONCENTERSEARCHDocumentationExperimentalDataAnalystOneofthemostdifficulttopicsinallofdataanalysisinthephysicalsciencesisfittingdatatononlinearmodels.Oftensuchfitsrequirelargecomputationalresourcesan
2、dgreatskill,patience,andintuitiononthepartoftheanalyst.Thesedifficultiesareoneofthereasonsthat,asweshallsee,thewholetopicofspectrallineshapesisstillaveryactivesubjectofresearchspanningthefieldsofchemistry,physics,astronomy,andmore.Inaddition,computational
3、methodsofnonlinearfittingarestillacurrentresearchtopicincomputerscience.However,sincesometimesnaturereallyisnonlinear,suchfitsareoftenunavoidable,andtheprinciplesandsometoolsfornonlinearfittingarethetopicsofthischapter.ThemainEDAprogramintroducedhereis,wh
4、ichaccomplishesfitstoarbitrarymodels.issimilartothefunctioninthepackagewhichisstandardwithMathematica.Theprimarydifferencesarethat:(1)recognizesEDA'sdataformat,includingerrorsinbothcoordinates;(2)estimateserrorsinfitparameters;(3)bydefaultdisplaysgraphica
5、linformationaboutthefit;and(4)usesanalgorithmthathasbeenoptimizedforspeedandstabilityforthetypesofnonlinearfitscommonlyperformedinthephysicalsciencesandengineering.5.1Introduction5.1.1OverviewofFindFitThepreviouschapter,"FittingDatatoLinearModelsbyLeast-S
6、quaresTechniques,"introducedthedistinctionbetweenlinearandnonlinearmodels.Tobrieflyreview,thetermsrefertothewayinwhichtheparameterstowhichwearefittingenterintothemodel.InthischapterwediscussnonlinearmodelsandtheEDAprogramthatcanoftenfindareasonablefittoth
7、em.Recallthatifsosisthesumofthesquaresoftheresiduals,thenweareseekingtheminimuminitsvalue.Ifwearefittingtoparametersa,a,...,a,theanswerisfoundbysolvingasetofsimultaneousequations.This,ingeneral,canbedoneanalytically,providedthemodeltowhichwearefittingisli
8、nearintheparameters.Similarly,whenthereareexpliciterrorsinthedata,weformthechi-squared,,andwesolvethecorrespondingequations.Thisagainwillbeanalyticforalinearfit.Foranonlinearfit,nosuchanalyticsolutionsarepossible,so
