简介：ConsiderabackwardheatequationinaboundeddomainΩR2withthenoisydataintheinitialtimegeometry.Theaimistofindthetemperaturefor0＜ε＜t＜T.Forthisill-posedproblem,theauthorsgiveacontinuousdependenceestimateofthesolution.Moreover,theconvergencerateoftheapproximatesolutionisalsogiven.

简介：一个方法为转换被描述在Laguerre多项式使用扩大并且把Mellin变换变换成Laplace变换的Mellin变换，然后，Laplace变换被合适的替换变换成第一个客气的卷绕旋转积分方程。那么获得的不可分的方程是一个提出病的问题，我们使用花键规则化解决它。方法的性能被在文学可得到的测试函数的倒置说明[J。Inst。数学。与Appl。20(1977)，p。73]，[J。数学。Comp。53(1989)，p。589]，[J。Sci。Stat。Comp。4(1983)，p。164]。方法的有效性被获得的结果显示出借助于桌子和图示威了。

简介：AnewmethodforapproximatingtheinerseLaplacetransformispresented.WefirstchangeourLaplacetransformequationintoaconvolutiontypeintegralequation,whereTikhonovregularizationtechniquesandtheFouriertransformationareeasilyapplied.WefinallyobtainaregularizedapproximationtotheinverseLaplacetransformasfinitesum

简介：这份报纸在外表涉及放射波浪地的重建一在上述的领域的边界的部分上从Cauchy数据的知识围住二维或三维的领域。它被Cauchy问题为Helmholtz方程描述。由使用Dirichlet-to-Neumann地图，这个问题与紧缩的操作员被转变成一个操作员方程。我们严厉地认为紧缩的操作符的单个值的asymptotic行为正当。然后，有规则化的一个设计方法被使用解决操作员方程，并且规则化方法的集中被讨论。最后，几个数字例子被举说明途径。结果证明算法是有效的。

简介：Inthispaper,weconsidertheCauchyproblemfortheLaplaceequation,whichisseverelyill-posedinthesensethatthesolutiondoesnotdependcontinuouslyonthedata.AmodifiedTikhonovregularizationmethodisproposedtosolvethisproblem.Anerrorestimatefortheaprioriparameterchoicebetweentheexactsolutionanditsregularizedapproximationisobtained.Moreover,anaposterioriparameterchoiceruleisproposedandastableerrorestimateisalsoobtained.Numericalexamplesillustratethevalidityandeffectivenessofthismethod.

简介：Inthispaper,weconsideraninversescatteringproblemforanobstacleDR^2withRobinboundarycondition.Byapplyingthepointsource,wegivearegularizingmethodtorecoverthescatteredfieldfromthefar-fieldpattern.Numericalimplementationsarealsopresented.

简介：这份报纸的目的是在在SPECT重建治好TV模型的staircasing人工制品调查infimal卷绕旋转规则化的能力。我们作为一个凸的三块的优化问题与infimal卷绕旋转规则化提出SPECT重建的问题并且以涉及它的客观函数的函数的最近操作符由定点方程的一个系统描绘它的解决方案。我们然后基于定点方程开发一个新奇定点最近算法。而且，我们介绍古典MLEM(最大可能性的的期望最大化)激发的一个preconditioning矩阵算法。我们证明建议算法的集中。数字结果被包括证明infimal卷绕旋转规则化能够有效地减少staircasing人工制品，当以signal-to-noise比率和系数恢复对比维持可比较的图象质量时。

简介：Regularizationmethodisaneffectivemethodforsolvingill-posedequation.Inthispapertheunbiasedestimationformulaofunitweightstandarddeviationintheregularizationsolutionisderivedandtheformulaisverifiedwithnumericalcaseof1000sampledatabyuseofthetypicalill-posedequation,i.e.theFredholmintegrationequationofthefirstkind.

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简介：Tomakeuseofthepriorknowledgeoftheimagemoreeffectivelyandrestoremoredetailsoftheedgesandstructures,anovelsparsecodingobjectivefunctionisproposedbyapplyingtheprincipleofthenon-localsimilarityandmanifoldlearningonthebasisofsuper-resolutionalgorithmviasparserepresentation.Firstly,thenon-localsimilarityregularizationtermisconstructedbyusingthesimilarimagepatchestopreservetheedgeinformation.Then,themanifoldlearningregularizationtermisconstructedbyutilizingthelocallylinearembeddingapproachtoenhancethestructuralinformation.Theexperimentalresultsvalidatethattheproposedalgorithmhasasignificantimprovementcomparedwithseveralsuper-resolutionalgorithmsintermsofthesubjectivevisualeffectandobjectiveevaluationindices.

简介：WeconsidertheproblemK(x)uxx=utt,0

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简介：Imagerestorationisoftensolvedbyminimizinganenergyfunctionconsistingofadata-fidelitytermandaregularizationterm.Aregularizedconvextermcanusuallypreservetheimageedgeswellintherestoredimage.Inthispaper,weconsideraclassofconvexandedge-preservingregularizationfunctions,I.e.,multiplicativehalf-quadraticregularizations,andweusetheNewtonmethodtosolvethecorrespondinglyreducedsystemsofnonlinearequations.AteachNewtoniterate,thepreconditionedconjugategradientmethod,incorporatedwithaconstraintpreconditioner,isemployedtosolvethestructuredNewtonequationthathasasymmetricpositivedefinitecoefficientmatrix.Theigenvalueboundsofthepreconditionedmatrixaredeliberatelyderived,whichcanbeusedtoestimatetheconvergencespeedofthepreconditionedconjugategradientmethod.Weuseexperimentalresultstodemonstratethatthisnewapproachisefficient,andtheeffectofimagerestorationisr0easonablywell.

简介：Inthispaperweconsideranon-standardinverseheatconductionproblemfordeterminingsurfaceheatfluxfromaninteriorobservationwhichappearsinsomeappliedsubjects.Thisproblemisill-posedinthesensethatthesolution(ifitexists)doesnotdependcontinuouslyonthedata.AFouriermethodisappliedtoformulatearegularizedapproximationsolution,andsomesharperrorestimatesarealsogiven.

简介：有一个更合适的操作员的一个修改规则化算法基于散布原则的Mie在激光粒子sizer从轻散布的数据为粒子尺寸分发(PSD)的倒置被建议。概括交叉验证(GCV)方法和L曲线方法被用于决定规则化参数。连续在松驰上(SOR)反复的方法被用来增加集成的结果的精确和稳定性。模仿的结果基于修改算法在与为九件标准微粒样品，他们的混合物以及三天赋测量的试验性的数据的一个好协议有不规则的形状的微粒材料，显示这个修改规则化方法为从相应轻散布的数据的PSD的模拟不仅可行而且有效。

简介：在这份报纸，反复的方法为近似解决在Banach空间包含m-accretivemappings的提出病的非线性的操作员方程被考虑的一种修改牛顿类型。方法的集中率被获得基于一规则化参数的一种priori选择。我们的分析不基于印射的规范的两重性的顺序的连续性。