18704.一類(lèi)變異型chebyshevhalley迭代法的收斂性

1、一類(lèi)變異型ChebyshevHalley迭代法的收斂性ConvergenceofthevariantsofaChebyshev’’1’1le3t11eiantsOShevllalley●●‘●一●lteratl011tamlly作者：包振威Author：BaoZhenwei指導(dǎo)教師：坌壹?jí)橲upervisor：XuXiubin專(zhuān)業(yè)：計(jì)算數(shù)學(xué)學(xué)位：理學(xué)碩士授予單位：浙江師范大學(xué)Major：——Computational—Mathemati

2、csDegree：MasterofScienceInstitute：——ZhejiangNormalUniversity——May2015AbstractInformationdevelopmentisveryrapidinmodernsocietyiterativemethodsforsolvingnonlinearproblemsarealsotobesynchronizedwiththerapidinformationdevelo

3、pmentSo，howtoincreasethespeedofiteration，determinetheconvergencerangeandreducetheiterationcosttakeakeypartinthecomputationalmathematicsThisthesisexploredthesemilocalconvergenceofChebyshevHaUeytypemethods，expandedtheconve

4、rgencerangeandacceleratedtheconvergencespeedThespecificcontentsareasfollows：InChapter1，weintroducedHaueymethod，ChebyshevmethodandChebyshevHalleytypemethods，whichincludethebasicconcepts，orderofconvergence，convergencecrite

5、riaandsomerelevantresultsinBanachspaceWealsopresentedthelayoutofthisthesisInChapter2，underconditionIIFⅣ(z)|I≤u(1lxll)，wediscussedtheconvergenceofthevariantsofaCheby’shevHalleyiterationfamilyTheconvergencecriterionandsemi

6、localconvergencewereobtainedFinallytheimpactofthechangeofparameterOLontheconvergenceradiuswasanalyzed，SOakindofchoosingcriterionfortheparameterwasprovidedThetechniqueusedistodecomposetheCheb7shevHalleytypeiterativeintotw

7、oparts，thefirstpartissimpleNewtoniterationwhichcanbesolvedbytheliteratureknowledgedirectlyandthesecondpartisthekeypart，whichwasinvestigatedbyusingamonotonicsequenceteducethenumberofiterationsandobtaintheconvergenceresult

8、InChapter3，wedemonstratedtheChebyrshevHaUeytypeiterativemethodsunderthecentralLipschitzcondition，|IF7(za，o)一1IFⅣ(∥)一FⅣ(z口，o)】|I≤LIlY—za，oII，Vy∈QTheconvergenceanderrorswereanalysedbyusingrecursivesequencesAtlast，bycombini

9、ngNewtonlikemethodsandChebyshevHalleytypeiterativemethodsinthecaseswhenthefirstorderderivativeexistsbutthesecondorderderivativedoesnotexist，westudiedthecomputationalcostreductionandthesimplificationofiterationconditionKe