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: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.
简介:1.IntroductionandMainResultSincethedefinitiononthecompleteconvergencewasintroducedbyHsuandRobbins[1],therehavebeenmanyauthorswhodevotethemselvestothestudyonthisconvergenceofiidrandomvariables,seeGut[2,3],BaiandSu[4]andLin[5].Meanwhile,somescholarshav...
简介:Withtheintegral-levelapproachtoglobaloptimization,aclassofdiscon-tinuouspenaltyfunctionsisproposedtosolveconstrainedminimizationproblems.InthispaperweproposeanimplementablealgorithmbymeansofthegoodpointsetofuniformdistributionwhichconquersthedefaultofMonte-Carlomethod.Atlastweprovetheconvergenceoftheimplementablealgorithm.
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.