简介：Aformulationofadifferentialequationasprojectionandfixedpointpi-Memalloivsapproximationsusinggeneralpiecnvisefunctions.Weproneexistenceanduniquenessoftheupproximatesolution*convergenceintheL2normandnodalsupercnnvergence.TheseresultsgeneralizethoseobtainedearlierbyHulmeforcontinuouspiecevjisepolynomialsandbyDelfour-Dubeaufordiscontinuouspieceuiisepolynomials.Adualityrelationshipforthetwotypesofapproximationsisalsogiven.

简介：Inthispaper,byusinganewprojection,weconstructavariantofZhang’salgorithmandproveitsconvergence.Specially,thevariantofZhang’salgorithmhasquadraticterminationandsuperlinearconvergenceraleundercertainconditions.Zhang’salgorithmhasn’ttheseproperties.

简介：Inthispaper,wepresentsomesufficientconditionsforconstructingthebasesoftheleftandtherightspacestoensurethefeasibilityoftheobliqueprojectionmethodandtheextendedobliqueprojectionmethod.

简介：Inthispaperwestudytheperturbationboundoftheprojection(WA)(WA)+,whereboththematricesAandWaregivenwithWpositivediagonalandseverelystiff.Whentheperturbedmatrix(A)=A+δAsatisfyseveralrowrankpreservingconditions,wederiveanewperturbationboundoftheprojection.

简介：quasistatic一致设计被做为不平表面的粘附描绘有效连贯的地区行为。在一致设计的上下文，为一个不平的接口的一致连贯的地区(HCZ)的拖拉对分离关系能在显微镜的粘附和decohesion进程期间由于不稳定性是高度摆动的。不稳定性被发现不仅个别地而且一起发生在粘合剂之中微粗糙的接触，导致广泛的精力驱散。基于HCZ关系的行为，为在不平表面的粘附描述导致不稳定性的精力驱散的一个框架被建议阐明明显的接口粘附上的粗糙的效果。二个非维的参数，与粗糙形态学有关的伪和与aw分发有关的n，被识别为控制精力驱散很关键。为浅粗糙和强壮的内在的粘合剂力量的一个接口，如果我们使它更不平，接口粘附能更强壮(减少伪)或降低它的aw密度(增加的n)。HCZ设计方法能潜在地被扩大并且采用了为与多尺度的浅粗糙设计表面从内在的粘附性质衔接明显的粘附。

简介：ConsiderL2-projectionuhofuton-degreefiniteelementspaceonone-dimensionaluniformgrids.TwodifferentclassesoftheorthogonalexpansioninanelementforconstructingasuperclosetofunctionuhareproposedandthensuperconvergenceforbothuhandDuhareproved.Whennisoddandnoboundaryconditionsareprescribed,thenuhisofsuperconvergenceatn+1orderGausspointsGn+1ineachelement.Whennisevenandfunctionvaluesontheboundaryareprescribed,thenuhisofsuperconvergenceatn+1orderpointsZn+1ineachelement.Iftheotherboundaryconditionsaregiven,thentheconclusionsarevalidinallelementsthatitsdistancefromtheboundary≥ch|lnh|.Theaboveconclusionsarealsovalid.forn-dergreerectangularelementQ1（n）.

简介：在这篇论文，我们与与凸的限制解决最小化问题的准确的步尺寸统治在坡度设计方法上给一些集中结果。特别，我们看那客观函数是否是凸的，它的坡度是Lipschitz连续，然后，这个方法与围住的准确的步尺寸生产的重复的整个顺序收敛到担心的问题的一个解决方案。

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。

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简介：Arevisedconjugategradientprojectionmethodfornonlinearinequalityconstrainedoptimizationproblemsisproposedinthepaper,sincethesearchdirectionisthecombinationoftheconjugateprojectiongradientandthequasi-Newtondirection.Ithastwomerits.Theoneisthattheamountofcomputationislowerbecausethegradientmatrixonlyneedstobecomputedonetimeateachiteration.Theotheristhatthealgorithmisofglobalconvergenceandlocallysuperlinearconvergencewithoutstrictcomplementaryconditionundersomemildassumptions.Inadditionthesearchdirectionisexplicit.

简介：在这篇文章，修理了点asymptotically概括了伪--nonexpansivemappings和平衡问题基于一个单调设计算法被调查。没有紧密的帮助，强壮的集中定理在反射Banach空格的框架被建立。

简介：ThepurposeofthispaperistostudythesuperconvergencepropertiesofRitz-Volterraprojection.ThroughconstructionanewtypeofGreenfunctionandmakinguseofitspropertiesandtheprincipleofduality,thepaperprovesthattheRitz-Volterraprojectiondefinedonr-1orderfiniteelementspacesofLagrangetypeinoneandtwospacevariablecasespossessesO(h2r~2)orderandO(h4+1|Inh|)ordernodalsuperconvergence,respectively,andthesametypeofsuperconver-genceresultsaredemonstratedforthesemidiscretefinitedementapproximatesolutionsofSoboleve-quations.

简介：Testingequalityofcovariancematrixhaslongbeenaninterestingissueinstatisticsinference,Toovercomethesparsenessofdatapointsinhigh-dimensionalspaceanddealwiththegeneralcases,theauthorsuggestsseveralprojectionpursuittypestatistics.Someresultsonthelimitingdistidbutionsofthestatisticsareobtained.Somepropertiesofbootstrapapproximationareinvestigated.Furthermore,forcomputationalreasonsanapproximationforthestatisticsbasedonnumber-theoreticroethodisapplied.Severalsimulationexperimentsareperformed.

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简介：在这份报纸，我们与本地设计稳定(LPS)为不可压缩的流动问题在有限元素方法的分析考察最近的开发。这些方法保存古典基于剩余的稳定(RBS)的赞成稳定性和近似性质技术但是避免在稳定术语的速度和压力的强壮的联合。LPS方法属于对称的稳定技术的班并且可以作为变化多尺度的方法被描绘。在这个工作，我们总结最重要priori这估计稳定计划的班在过去的6年里发展了。我们认为Stokes方程，Oseenlinearization和海军司烧是方程。而且，我们把它用于最佳的控制问题与线性(ized)流动问题，后来，稳定的对称导致好特征操作“discretize”并且“优化”路程。[从作者抽象]

简介：WeextendtheobliqueprojectionmethodgivenbyY.Saadtosolvethegeneralizedleastsquaresproblem.Thecorrespondingobliqueprojectionoperatorispresentedandtheconvergencetheoremsareproved.SomenecessaryandsufficientconditionsforcomputingthesolutionortheminimumN-normsolutionofthemin||Ax-b||M2havebeenproposedaswell.

简介：Inthispaper,weprovideanewgeneralizedgradientprojectionalgorithmfornonlinearprogrammingproblemswithlinearconstraints.Thisalgorithmhassimplestructureandisverypracticalandstable.Undertheweakerassumptions,wehaveprovedtheglobalconvergenceofouralgorithm.

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简介：Efficientoptimizationstrategyofmultibodysystemsisdevelopedinthispaper.AugmentedLagrangemethodisusedtotransformconstrainedoptimalproblemintounconstrainedformfirstly.Thenmethodsbasedonsecondordersensitivityareusedtosolvetheunconstrainedproblem,wherethesensitivityissolvedbyhybridmethod.Generalized-αmethodandgeneralized-αprojectionmethodforthedifferential-algebraicequation,whichshowsmoreefficientpropertieswiththelagertimestep,arepresentedtogetstatevariablesandadjointvariablesduringtheoptimizationprocedure.Numericalresultsvalidatetheaccuracyandefficiencyofthemethodsispresented.

简介：ThepurposeofthispaperistostudythestabilityandapproximationpropertiesofRitz-Volterraprojection.ThroughconstructinganewtypeofGreenfunctionsandmakinguseofvariouspropertiesandestimatesrelatedwiththefunctions,weprovethattheRitz-Volterraprojectiondefinedonthefinite-dimensionalsubspaceS_hofH_o~1possessestheW_p~1-stabilityandtheoptimalapproximationpropertiesinW_p~1andL_pfor2≤p≤∞.Ourresults,inthispaper,canbeappliedtothefiniteelementapproximationsformanyevolutionequationssuchasparabolicandhyperbolicintegrodifferentialequations,Sobolevequationsandvisco-elasticity,etc.