计算反演问题中的优化与正则化方法及其应用（国内英文版）

图书标准信息

• 作者 王彦飞、[俄]亚哥拉（Anatoly G.Yagola）、杨长春 编
• 出版社 高等教育出版社
• 出版时间 2010-05
• 版次 1
• ISBN 9787040285154
• 定价 79.00元
• 装帧 精装
• 开本 16开
• 纸张 胶版纸
• 页数 350页
• 字数 620千字
• 正文语种 英语

【内容简介】

《计算反演问题中的优化与正则化方法及其应用》内容简介：OptimizationandRegularizationforComputationalInverseProblemsandApplicationsfocusesonadvancesininversiontheoryandrecentdevelopmentswithpracticalapplications,particularlyemphasizingthecombinationofoptimizationandregularizationforsolvinginverseproblems.Thisbookcoversboththemethods,includingstandardregularizationtheory,Fejerprocessesforlinearandnonlinearproblems,thebalancingprinciple,extrapolatedregularization,nonstandardregularization,nonlineargradientmethod,thenonmonotonegradientmethod,subspacemethodandLiegroupmethod;andthepracticalapplications,suchasthereconstructionproblemforinversescattering,molecularspectradataprocessing,quantitativeremotesensinginversion,seismicinversionusingtheLiegroupmethod,andthegravitationallensingproblem.
Scientists,researchersandengineers,aswellasgraduatestudentsengagedinappliedmathematics,engineering,geophysics,medicalscience,imageprocessing,remotesensingandatmosphericsciencewillbenefitfromthisbook.

【作者简介】

编者：王彦飞（俄国）亚哥拉（AnatolyG.Yagola）杨长春

Dr.YanfeiWangisaProfessorattheInstituteofGeologyandGeophysics,ChineseAcademyofSciences,China.
Dr.Sc.AnatolyG.YagolaisaProfessorandAssistantDeanofthePhysicalFaculty,LomonosovMoscowStateUniversity,Russia.
Dr.ChangchunYangisaProfessorandViceDirectoroftheInstituteofGeologyandGeophysics,ChineseAcademyofSciences,China.

【目录】

PartIIntroduction
1InverseProblems,OptimizationandRegularization:AMulti-DisciplinarySubject
YanfeiWangandChangchunYang
1.1Introduction
1.2Examplesaboutmathematicalinverseproblems
1.3Examplesinappliedscienceandengineering
1.4Basictheory
1.5Scientificcomputing
1.6Conclusion
Referertces
PartIIRegularizationTheoryandRecentDevelopments

2Ill-PosedProblemsandMethodsforTheirNumericalSolution
AnatolyG.Yagola
2.1Well-posedandill-posedproblems
2.2Definitionoftheregularizingalgorithm
2.3Ill-posedproblemsoncompactsets
2.4Ill-posedproblemswithsourcewiserepresentedsolutions
2.5Variationalapproachforconstructingregularizingalgorithms
2.6Nonlinearill-posedproblems
2.7Iterativeandothermethods
References

3InverseProblemswithAPrioriInformation
VladimirV.Vasin
3.1Introduction
3.2Formulationoftheproblemwithaprioriinformation
3.3ThemainclassesofmappingsoftheFejertypeandtheirproperties
3.4Convergencetheoremsofthemethodofsuccessiveapproximationsforthepseudo-contractiveoperators
3.5ExamplesofoperatorsoftheFejertype
3.6Fejerprocessesfornonlinearequations
3.7Appliedproblemswithaprioriinformationandmethodsforsolution
3.7.1Atomicstructurecharacterization
3.7.2Radiolocationoftheionosphere
3.7.3Imagereconstruction
3.7.4Thermalsoundingoftheatmosphere
3.7.5Testingawellbore/reservoir
3.8Conclusions
References

4RegularizationofNaturallyLinearizedParameterIdentificationProblemsandtheApplicationoftheBalancingPrinciple
HuiCaoandSergeiPereverzyev
4.1Introduction
4.2DiscretizedTikhonovregularizationandestimationofaccuracy
4.2.1Generalizedsourcecondition
4.2.2DiscretizedTikhonovregularization
4.2.3Operatormonotoneindexfunctions
4.2.4Estimationoftheaccuracy
4.3Parameteridentificationinellipticequation
4.3.1Naturallinearization
4.3.2Datasmoothingandnoiselevelanalysis
4.3.3Estimationoftheaccuracy
4.3.4Balancingprinciple
4.3.5Numericalexamples
4.4Parameteridentificationinparabolicequation
4.4.1Naturallinearizationforrecoveringb(x)=a(u(T,x))
4.4.2Regularizedidentificationofthediffusioncoefficienta(u)
4.4.3Extendedbalancingprinciple
4.4.4Numericalexamples
References

5ExtrapolationTechniquesofTikhonovRegularization
TingyanXiao,YuanZhaoandGuozhongSu
5.1Introduction
5.2Notationsandpreliminaries
5.3Extrapolatedregularizationbasedonvector-valuedfunctionapproximation
5.3.1ExtrapolatedschemebasedonLagrangeinterpolation
5.3.2ExtrapolatedschemebasedonHermitianinterpolation
5.3.3Extrapolationschemebasedonrationalinterpolation
5.4Extrapolatedregularizationbasedonimprovementofregularizingqualification
5.5Thechoiceofparametersintheextrapolatedregularizingapproximation
5.6Numericalexperiments
5.7Conclusion
References

6ModifiedRegularizationSchemewithApplicationinReconstructingNeumann-DirichletMapping
PingliXieandJinCheng
6.1Introduction
6.2Regularizationmethod
6.3Computationalaspect
6.4Numericalsimulationresultsforthemodifiedregularization
6.5TheNeumann-Dirichletmappingforellipticequationofsecondorder
6.6ThenumericalresultsoftheNeumann-Dirichletmapping
6.7Conclusion
References
PartIIINonstandardRegularizationandAdvancedOptimizationTheoryandMethods

7GradientMethodsforLargeScaleConvexQuadraticFunctions
YaxiangYuan
7.1Introduction
7.2Ageneralizedconvergenceresult
7.3ShortBBsteps
7.4Numericalresults
7.5Discussionandconclusion
References

8ConvergenceAnalysisofNonlinearConjugateGradientMethods
YuhongDai
8.1Introduction
8.2Somepreliminaries
8.3Asufficientandnecessaryconditionon鈑
8.3.1Propositionofthecondition
8.3.2Sufficiencyof(8.3.5)
8.3.3Necessityof(8.3.5)
8.4Applicationsofthecondition(8.3.5)
8.4.1Property(#)
8.4.2Applicationstosomeknownconjugategradientmethods
8.4.3Applicationtoanewconjugategradientmethod
8.5Discussion
References

9FullSpaceandSubspaceMethodsforLargeScaleImageRestoration
YanfeiWang,ShiqianMaandQinghuaMa
9.1Introduction
9.2Imagerestorationwithoutregularization
9.3Imagerestorationwithregularization
9.4Optimizationmethodsforsolvingthesmoothingregularizedfunctional
9.4.1Minimizationoftheconvexquadraticprogrammingproblemwithprojection
9.4.2LimitedmemoryBFGSmethodwithprojection
9.4.3Subspacetrustregionmethods
9.5Matrix-VectorMultiplication(MVM)
9.5.1MVM:FFT-basedmethod
9.5.2MVMwithsparsematrix
9.6Numericalexperiments
9.7Conclusions
References
PartIVNumericalInversioninGeoscienceandQuantitativeRemoteSensing

10SomeReconstructionMethodsforInverseScatteringProblems
JijunLiuandHaibingWang
10.1Introduction
10.2Iterativemethodsanddecompositionmethods
10.2.1Iterativemethods
10.2.2Decompositionmethods
10.2.3Hybridmethod
10.3Singularsourcemethods
10.3.1Probemethod
10.3.2Singularsourcesmethod
10.3.3Linearsamplingmethod
10.3.4Factorizationmethod
10.3.5Rangetestmethod
10.3.6Noresponsetestmethod
10.4Numericalschemes
References

11InverseProblemsofMolecularSpectraDataProcessing
GulnaraKuramshina
11.1Introduction
11.2Inversevibrationalproblem
11.3Themathematicalformulationoftheinversevibrationalproblem
11.4Regularizingalgorithmsforsolvingtheinversevibrationalproblem
11.5Modelofscaledmolecularforcefield
11.6Generalinverseproblemofstructuralchemistry
11.7Intermolecularpotential
11.8Examplesofcalculations
11.8.1Calculationofmethaneintermolecularpotential
11.8.2PredictionofvibrationalspectrumoffullereneC240
References

12NumericalInversionMethodsinGeoscienceandQuantitative
RemoteSensing
YanfeiWangandXiaowenLi
12.1Introduction
12.2Examplesofquantitativeremotesensinginverseproblems:landsurfaceparameterretrievalproblem
12.3Formulationoftheforwardandinverseproblem
12.4Whatcausesill-posedness
12.5Tikhonovvariationalregularization
12.5.1ChoicesofthescaleoperatorD
12.5.2Regularizationparameterselectionmethods
12.6Solutionmethods
12.6.1Gradient-typemethods
12.6.2Newton-typemethods
12.7Numericalexamples
12.8Conclusions
References

13Pseudo-DifferentialOperatorandInverseScatteringofMultidimensionalWaveEquation
HongLiu,LiHe
13.1Introduction
13.2Notationsofoperatorsandsymbols
13.3Descriptioninsymboldomain
13.4Liealgebraintegralexpressions
13.5Waveequationontheraycoordinates
13.6Symbolexpressionofone-waywaveoperatorequations
13.7Liealgebraexpressionoftraveltime
13.8Liealgebraintegralexpressionofpredictionoperator
13.9Spectralfactorizationexpressionsofreflectiondata
13.10Conclusions
References

14TikhonovRegularizationforGravitationalLensingResearch.
BorisArtamonov,EkaterinaKoptelova,ElenaShimanovskayaandAnatolyG.Yagola
14.1Introduction
14.2Regularizeddeconvolutionofimageswithpointsourcesandsmoothbackground
14.2.1Formulationoftheproblem
14.2.2Tikhonovregularizationapproach
14.2.3Aprioriinformation
14.3ApplicationoftheTikhonovregularizationapproachtoquasarprofilereconstruction
14.3.1Briefintroductiontomicrolensing
14.3.2Formulationoftheproblem
14.3.3ImplementationoftheTikhonovregularizationapproach
14.3.4NumericalresultsoftheQ2237profilereconstruction
14.4Conclusions
References
Index