简介:InthispaperwestudythecomputationalperformanceofvariantsofanalgebraicadditiveSchwarzpreconditionerfortheSchurcomplementforthesolutionoflargesparselinearsystems.Inearlierworks,thelocalSchurcomplementswerecomputedexactlyusingasparsedirectsolver.Therobustnessofthepreconditionercomesatthepriceofthismemoryandtimeintensivecomputationthatisthemainbottleneckoftheapproachfortacklinghugeproblems.InthisworkweinvestigatetheuseofsparseapproximationofthedenselocalSchurcomplements.TheseapproximationsarecomputedusingapartialincompleteLUfactorization.Suchanumericalcalculationisthecoreofthemulti-levelincompletefactorizationsuchastheoneimplementedinpARMS.Thenumericalandcomputingperformanceofthenewnumericalschemeisillustratedonasetoflarge3Dconvection-diffusionproblems;preliminaryexperimentsonlinearsystemsarisingfromstructuralmechanicsarealsoreported.
简介:Inthispaper,least-squaxesmirrorsymmetricsolutionformatrixequations(AX=B,XC=D)anditsoptimalapproximationisconsidered.Withspecialexpressionofmirrorsymmetricmatrices,ageneralrepresentationofsolutionfortheleast-squaresproblemisobtained.Inaddition,theoptimalapproximatesolutionandsomealgorithmstoobtaintheoptimalapproximationareprovided.
简介:AbstractFortheweaklyinhomogeneousacousticmediuminΩ={(x,y,z):z>0},weconsidertheinverseproblemofdeterminingthedensityfunctionρ(x,y).Theinversioninputforourinverseproblemisthewavefieldgivenonaline.Wegetanintegralequationforthe2-Ddensityperturbationfromthelinearization.Byvirtueoftheintegraltransform,weprovetheuniquenessandtheinstabilityofthesolutiontotheintegralequation.Thedegreeofill-posednessforthisproblemisalsogiven.
简介:M.Randic首先引入了Wiener.Hosoya指标,该指标可用于对分子的结构,性质和活跃性等方面进行研究.有且仅有一个顶点的度大于或等于3的树称为spider.本文对直径为d,且具有最大Wiener-Hosoya指标的spider进行了刻划.
简介:LetMbeapositivequaternionicKhlermanifoldofdimension4m.Wealreadyshowedthatifthesymmetryrankisgreaterthanorequalto[m/2]+2andthefourthBettinumberb_4isequaltoone,thenMisisometrictoHP~(m).Thegoalofthispaperistoreportthatwecanimprovethelowerboundofthesymmetryrankbyoneforhighereven-dimensionalpositivequaternionicKahlermanifolds.Namely,itisshowninthispaperthatifthesymmetryrankofMwithb_4(M)=1isgreaterthanorequaltom/2+1form≥10,thenMisisometrictoHP~m.OneofthemainstrategiesofthispaperistoapplyamoredelicateargumentofFrankeltypetopositivequaternionicKhlermanifoldswithcertainsymmetryrank.
简介:Assumethatm≥2,pisaprimenumber,(m,p(p-1))=1,-1(Z/mZ)~*and[(Z/mZ)~*:]=4.Inthispaper,wecalculatethevalueofGausssumG(X)=Σ_(x∈F_q~*)x(x)ζ_p~(T(x))overF_q,whereq=p~f,f=((m))/4xisamultiplicativecharacterofF_qandTisthetracemapfromF_qtoF_p.Underourassumptions,G(x)belongstothedecompositionfieldKofpinQ(ζm)andKisanimaginaryquarticabeliannumberfield.WhentheGaloisgroupGal(K/Q)iscyclic,wehavestudiedthiscycliceaseinanotherpaper:'Gausssumsofindexfour:(1)cycliccase'(acceptedbyActaMathematicaSinica,2003).Inthispaperwedealwiththenon-cycliccase.
简介:At-hyperwheel(t≥3)oflengthl(orW(t)lforbrevity)isat-uniformhypergraph(V,E),whereE={e1,e2,...,el}andv1,v2,...,vlaredistinctverticesofV=∪eii=1lsuchthatfori=1,...,l,vi,vi+1∈eiandei∩ej=P,j∈/{i1,i,i+1},wheretheoperationonthesubscriptsismodulolandPisavertexofVwhichisdifferentfromvi,1≤i≤l.Inthispaper,theminimumcoveringproblemofMCλ(3,W(3)4,v)isinvestigated.DirectandrecursiveconstructionsonMCλ(3,W(3)4,v)arepresented.Thecoveringnumbercλ(3,W(3)4,v)isfinallydeterminedforanypositiveintegersv≥5andλ.