带限函数外推算法研究

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1、北京交通大学硕士学位论文带限函数外推算法研究姓名：杨健申请学位级别：硕士专业：计算数学指导教师：渠刚荣20080601ABSTRACTABSTRACT：Letfbeafiniteenergyfunctiondefinedovertherealline(f∈r)：lIf(t)12

2、ecanexpecttorecoverf(t)，whent仨【-T，T】fromg．Hence，thecontinuousextrapolationproblemis(undertheconditionsstatedabove)isfind厂(f)，t萑【-T，T】，given厂(≠)，t∈【-T，明．Whenthesignaldoesnotincludethefrequencywhichishigherthansomefrequency,wecallthesignalfrequency-limitedsignalorband—l

3、imitedsignal(thatisband-limitedfunction)．Band-limitedfunctionextrapolationisextensivelyappliedinspectrumestimate[71，angle．1imitedimagereconstruction[351,andmanyotherareas．PapoulisandGerchebrgpresentedaniterativealgorithminwhichtheiterationconvergestotheextrapolationof

4、theband·limitedsignaliftheinitialdataisnoise．fleet地1．InordertoimplementtheGerchberg．Papoulisalgorithmfortheextrapolationofone-dimensionalband—limitedsignals，SanzandHuangsuggestedaconjecture(proofedin【31】)forthediscreteapproximationofGerchberg—Papoulisalgorithml31．Ther

5、earealsomanyotherextrapolationalgorithms[4】【8】．Inthispaper,twonewalgorithmsalesuggestedtosolvetheproblemofband—limitedextrapolation，oneisLandweberiterativealgorithm，anotheriseonjugategradientmethod．Then，convergenceofthetwonewschemesisdemonstrated．Itisalsoproofedthatwh

6、enchoosingtherelaxtioncoefficientsofLandweberiterationas1,thismethodisequivalenttotheGerchberg-Papoulisalgorithmforband-limitedsignalextrapolation．Finallyanumberofillustrativenumericalexamplesalepresentedanddiscussed．Whenwecomputenumericalexamples，webasedonSanzandHuan

7、g’Stheoremtoimplementournewalgorithms．TheresultsshowthatLandweberiterativemethodandconjugategradientiterativeschemealebothmoreefficientthanGerchberg—Papoulisalgorithm．KEYWORDS：band-limitedfunctionextrapolation；Gerchberg·Papoulisalgorithm；regularizationtheory；Landweber

8、iteration；conjugategradientmethodCLASSNO：0174．2：0175．5学位论文版权使用授权书本学位论文作者完全了解北京交通大学有关保留、使用学位论文的规定。特授权北京交通大学可以将学位论文的全部或部分内容编入有