典則TSVD方法及其相關(guān)問題.pdf

1、上海大學(xué)碩士學(xué)位論文典則TSVD方法及其相關(guān)問題姓名：張寧申請(qǐng)學(xué)位級(jí)別：碩士專業(yè)：計(jì)算數(shù)學(xué)指導(dǎo)教師：賀國(guó)強(qiáng)20030401上海大學(xué)碩士研究生學(xué)位論文IIAbstractThisthesisconsidersanewTSVDformmethod—CanonicalTSVDMethodforsolvinglineari1】一posedinverseproblemsResultsrelatedtoitstheoreticalanalysisa

2、ndnumericalexamplesareobtainedChapteronebrieflyintroducesseveralregularizationmethodsandparameterchoicemethodsdiscussedinthisthesisaftergivingtheconceptionsofIll—posedInverseProblemandRegularizaionThemainworkofthisthesis

3、isdescribedindetailinchaptertwochapterthreeandchapterfourChaptertwodiscussescanonicalTSVDmethodinfinitedimemsionalspaceswhenonlytheright—handsideisnoisyTheorem221provesthismethodcanleadtooptimalconvergenceratewithoutanya

4、ssumptionMoreover，section23givesseveralnumericalexampleswithbeautifulresultsbyusingthismethod，whichdemonstratethattheabovetheoreticalconclusionsholdinpracticalcomputationalsettingsChapterthreeconcernsthecaseofbothperturb

5、edoperatorsandnoisydataOuranalysisbeginswith肛orderA—smoothregularizationbecauseitwillbecomecanonicalTSVDmethodwhenptendstoinfinityThecovergenceandconvergencerateofAsmoothregularizationareprovedindetail，whenusingbothsemia

6、posterioriMorozovDiscrepancyandfullyaposterioriMorozovDiscrepancytoselectreganlarizationparametersAfterthat，itisfoundthat，when“tendstoinfinity，theconclusionsderivedfromporderAsmoothregularizationcannotdirectlyleadtesults

7、ofcanonicalTSVDmethodTherefore，anewmethodwillbeinneedtodiscusscanonicalTSVDmethodwhenboththeoperatorsareperturbedandthedataarenoisyHowever，fortheabovecase，severalnumericalexamplesarealsogiven，andtiieirsatisfactoryresults

8、areobtainedbymeansofcanonicalTSVDmethod，whichdemonstratethatthismethodisalsoeffectiveforsolvingill—posedequationswithbothperturberbedoperatorsandnoisydataChapterfourmakessystematicintroduction，analysisanddiscussionofapre

9、sentlypopu—larerror—freeformparameterchoicemethod—L—curveCriterionanddetailedlydiscussesitforcanonicalTSVDmethodAftercolligation，understandingandanalysisofmanygoodandbadevaluationsofit，thiscriterionisappliedtofourdiffere

10、ntregularizationmethods，ie，Tikhonovregularization，implicititerativemethod，truncatedSVDandcanonicalTSVDmethodespeciallythelastoneWithsomenumericalexamples，fournumericalmthodstofindthecorneronL—curvearediscussedandcompared

11、withMorozovDiscrepancyOurconclusionisthat，ingeneral，thenumericalresultsobtainedbymeansofL—curveCriterionarenotsogoodasthoseobtainedbyMorozovDiscrepancy，andforsomediscreteregularizationmethods，thisparameterchoicemethodsti