简介：AclassofparallelnonlinearmultisplittingAORmethodsissetupbydirectlymultisplittingthenonlinearmappingF:DCR^n→R^nforsolvingthenonlinearsystemofequationsF(x)=0.Thedifferentchoicesoftherelaxationparameterscanyieldalltheknownandalotofnewrelaxationmethodsaswellasalotofnewrelaxationparallelnonlinearmultisplittingmethods.Thetwo-sidedapproximationpropertiesandtheinfluencesonconvergencefromtherelaxationparametersaboutthenewmethodsareshown,andthesufficientconditionsguaranteeingthemethodstoconvergegloballyarediscussed.Finally,alotofnumericalresultsshowthatthemethodsarefeasibleandefficient.

简介：Anewsmoothingmethodisproposed.Thesmoothingprocessadaptstoimagecharacteristicsandisgoodatpreservinglocalimagestructures.Moreimportantly,inthetheoryundertheconditionsweakerthanthoseintheoriginalKacanovmethodanapproximalsequenceofsolutionstothevariationalproblemscanbeconstructedandtheglobalconvergencecanbeproved.AndtheconditionsinthepapersofSchn6rr(1994)andHeers,etal(2001)arediscussed.Numericalsolutionsofthemodelaregiven.

简介：AnecessaryandsufficientconditionofconvergenceforthemodifiedSzasz-Mirakjanoperatorisestab-lished.

简介：在这篇文章，为克利福德的一个足够的条件继续部分会聚被建立，并且一些应用被给。

简介：ThepurposeofthispaperistostudythepointwiseandalmosteverywhereconvergenceoftheCesaromeans(C,δ)ofFourier-Jacobiexpansions,themaintermoftheLebesgueconstantofthe(C,8)meansfor-1<δ≤α+1/2isobtained.WiththeaidofthegeneralizedtranslationintermsofJacobipolynomials,pointwiseconvergencetheoremsofthe(C,δ)meansforδ>α+1/2andequiconvergencetheoremsfor-1<δ≤α+1/2areproved.TheanaloguesoftheLebesgue,SalemandYoungtheoremsoftheCesaromeansatthecriticalindexδ=α+1/2areestablished.

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简介：1.IntroductionandMainResultSincethedefinitiononthecompleteconvergencewasintroducedbyHsuandRobbins[1],therehavebeenmanyauthorswhodevotethemselvestothestudyonthisconvergenceofiidrandomvariables,seeGut[2,3],BaiandSu[4]andLin[5].Meanwhile,somescholarshav...

简介：Wediscussestimatesfortherateofconvergenceofthemethodofsuccessivesubspacecorrectionsintermsofconditionnumberestimateforthemethodofparallelsubspacecorrections.Weprovideupperboundsandinaspecialcase,alowerboundforpreconditionersdefinedviathemethodofsuccessivesubspacecorrections.

简介：Withtheintegral-levelapproachtoglobaloptimization,aclassofdiscon-tinuouspenaltyfunctionsisproposedtosolveconstrainedminimizationproblems.InthispaperweproposeanimplementablealgorithmbymeansofthegoodpointsetofuniformdistributionwhichconquersthedefaultofMonte-Carlomethod.Atlastweprovetheconvergenceoftheimplementablealgorithm.

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简介：Inthispaperweconsidertheglobalconvergenceofanyconjugategradientmethodoftheformd1=-g1,dk+1=-gk+1+βkdk(k≥1)withanyβksatisfyingsumeconditions,andwiththestrongwolfelinesearchconditions.Undertheconvexassumptionontheobjectivefunction,weprevethedescenfpropertyandtheglobalconvergenceofthismethod.

简介：ItisprovedinthispaperthattheapproximatesolutionofthediscontinuousGalerkinmethoddoesconvergeeventheexactsolutionofthefirstorderhyperbolicequationisdiscontinuous.

简介：1.IntroductionactEbeaHa~tOPologicalspaceandmamdritemeasureonitsBorela-algebraB(E).In[11,MOSCointroducedthefollowingnow-calledMoscoconvergenceofsyllUnetricac~l~:tlf621i.t,..2.1].AsequenceofsynUnetricbilinearforms(En,D(en)),nEN,issaidtoMO8coconvergetoa...

简介：LetthelinearsystemAx=bwherethecoefficientmatrixA=(aij)∈Rm,nisanL-ma-trix(thatis,aij>0（?）iandaij≤0（?）i≠j),A=I-L-U,Iistheidentitymatrix,-Land-Uare,respectively,strictlylowerandstrictlyuppertriangularpartsofA.In[1]theauthorsconsideredtwopreconditionedlinearsystems?x=（?）and?x=（?）

简介：Thecapabilityofmultilayerperceptrons(MLPs)forapproximatingcontinuousfunctionswitharbitraryaccuracyhasbeendemonstratedinthepastdecades.Backpropagation(BP)algorithmisthemostpopularlearningalgorithmfortrainingofMLPs.Inthispaper,asimpleiterationformulaisusedtoselecttheleamingrateforeachcycleoftrainingprocedure,andaconvergenceresultispresentedfortheBPalgo-rithmfortrainingMLPwithahiddenlayerandalinearoutputunit.Themonotonicityoftheerrorfunctionisalsoguaranteedduringthetrainingiteration.

简介：Theessenceofthelinearsearchisone-dimensionnonlinearminimizationproblem,whichisanimportantpartofthemulti-nonlinearoptimization,itwillbespendthemostofoperationcountforsolvingoptimizationproblem.Toimprovetheefficiency,wesetaboutfromquadraticinterpolation,combinetheadvantageofthequadraticconvergencerateofNewton'smethodandadopttheideaofAnderson-Bjorckextrapolation,thenwepresentarapidlyconvergencealgorithmandgiveitscorrespondingconvergenceconclusions.Finallywedidthenumericalexperimentswiththesomewell-knowntestfunctionsforoptimizationandtheapplicationtestoftheANNlearningexamples.Theexperimentresultsshowedthevalidityofthealgorithm.

简介：ThispapergivestheweightedLpconvergencerateestimationsoftheGruenwaldinterpolatorypolynomialsbasedonthezerosofChebyshevpolymomialsofthefirstkind,andprovesthattheorderoftheestimationsisoptimalforp≥1.

简介：Inthepresentpaper,weintroduceSzász-Durrmeyer-BézieroperatorsMn,o(f,x),whichgeneralizethetionsofboundedvariation.OurresultextendsandimprovesthatofSahaiandPrasad[9]andGuptaandPant[3].

简介：Theobjectiveofthispaperistointroduceelementarydiscretereflectedbackwardequationsandtogiveasimplemethodtodiscretizeintimea(continuous)reflectedbackwardequation.Apresentationofnumericalsimulationsisalsodescribed.

简介：Inthispaper,westudytheconvergencerateoftwo-dimensionalBaskakovoperatorswithJacobiweightsmakinguseofmultivariatedecomposeskillsandresultsofone-dimensionalBaskakovoperators,andobtainthedirectapproximationtheorem.