两类非齐次不适定问题的正则化

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1、华中科技大学硕士学位论文两类非齐次不适定问题的正则化姓名：曾雪军申请学位级别：硕士专业：应用数学指导教师：黄永忠20090520kY7wy.>7V?_=Z!RtA

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6、ceanengineering,iatrologyimagingandsoon.Becausetheinstabilityoftheill-posedproblemscausesgreattroubleinnumericalcaculating,itisnecessarytointroduceregularization.Therearealreadyalotofmeth-odsofregularizationexisted,forexample,Tikhonovregularizationmethod,dispersemethod,projectionmet

7、hod,semi-groupmethod,Fouriermethod,waveletmethod,QRmethod.OnedimensionhomogeneousbackwardCauchyproblem(ut+Au=0,0

8、dofproblem,andmanysatisfactoryresultsareobtaned.However,Thereislessresearchonthecaseofnonhomogeneous,2dimensionandmulti-dimension,whichisjustthisthesisgoingtoconsider.ThisthesiswilldiscusstwoproblemsinHilbertspace:nonhomogeneousbackwardheatequationinrectangleregionandnonhomogeneousb

9、ackwardCauchyproblem.ThroughregularizingthembyusingQRmethodandQBVmethod,thethesisobtainscorrespondingerrorestimate.numericalexamplesaregivenatlast.Keywords:Ill-posedproblem,Nonhomogeneous,Regularization,QRmethod,QBVmethod.II
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