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:研究复杂系统要探索整体规律.本文指出:为此,需要对定性研究予以适当重视.文中给出一个表达式(E):S(n∑i=11i)=E(n),即自聚集、自组织,演化发展到新层次.此式用以描述复杂系统的结构形成及动态行为.还时其中"自聚集"的概念给以着重阐述.又分析了聚集的量对系统功能的影响,并给出表达式(C):11+12+…+1n>en2.然后,从生物、自然界、社会、工程等不同领域,解释可用(E)式概括的一些规律性现象;还从复杂系统的观点并借助(E)式讨论了对"从量变到质变"的进一步认识.最后,将复杂系统的自相似结构与分形自相似结构对比,指出一类复杂系统其结构的形成实质是由简单规则多次重复而来,即复杂寓于简单,且聚集、组织,再聚集、再组织……即(E)式多次重复,是形成一类复杂系统结构的基本规则.
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。