简介:Inthispaper,simultaneousuniformapproximationandmeanconvergenceofquasi-HermiteinterpolationanditsderivativebasedonthezerosofJacobipolynomialsareconsideredseparately.Thedegreesofthecorrespondingapproximationsarerespectivelygivenalso.Someknownresultsareimprovedaudextended.
简介:EllipticPDE-constrainedoptimalcontrolproblemswithL^1-controlcost(L^1-EOCP)areconsidered.TosolveL^1-EOCP,theprimal-dualactiveset(PDAS)method,whichisaspecialsemismoothNewton(SSN)method,usedtobeapriority.However,ingeneralsolvingNewtonequationsisexpensive.Motivatedbythesuccessofalternatingdirectionmethodofmultipliers(ADMM),weconsiderextendingtheADMMtoL^1-EOCP.TodiscretizeL^1-EOCP,thepiecewiselinearfiniteelement(FE)isconsidered.However,differentfromthefinitedimensionalL^1-norm,thediscretizedL^1-normdoesnothaveadecoupledform.Toovercomethisdifficulty,aneffectiveapproachisutilizingnodalquadratureformulastoapproximatelydiscretizetheL^1-normandL^2-norm.Itisprovedthattheseapproximationstepswillnotchangetheorderoferrorestimates.Tosolvethediscretizedproblem,aninexactheterogeneousADMM(ihADMM)isproposed.DifferentfromtheclassicalADMM,theihADMMadoptstwodifferentweightedinnerproductstodefinetheaugmentedLagrangianfunctionintwosubproblems,respectively.Benefitingfromsuchdifferentweightedtechniques,twosubproblemsofihADMMcanbeefficientlyimplemented.Furthermore,theoreticalresultsontheglobalconvergenceaswellastheiterationcomplexityresultso(1/k)forihADMMaregiven.Inordertoobtainmoreaccuratesolution,atwo-phasestrategyisalsopresented,inwhichtheprimal-dualactiveset(PDAS)methodisusedasapostprocessoroftheihADMM.Numericalresultsnotonlyconfirmerrorestimates,butalsoshowthattheihADMMandthetwo-phasestrategyarehighlyefficient.
简介:由在卡尔弗特和Gupta的非线性的accretivemappings的范围的和上使用不安理论,我们在答案u∈L~S的存在上学习抽象结果(包含p拉普拉斯算符操作员的非线性的边界价值问题的Ω),在此2≤s≤+∞,并且(2N)/(N+1)
L.魏和Z.的相应结果他。
简介:摘要:新型钙钛矿太阳能电池是一种新型清洁可再生能源,将其应用到实际生活中充分满足了社会节能、低碳、环保的发展要求。为此,文章在阐述新型钙钛矿太阳能电池基本构造的基础上,分析当前新型钙钛矿太阳能电池的研究进展和研究存在问题,并从提升新型钙钛矿太阳能电池转换效率、增强新型钙钛矿太阳能电池稳定性、降低新型钙钛矿太阳能电池污染性几个方面就其未来发展优化进行展望。
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