简介：LetGbeasimplegraphwithnverticesandλn（G）betheleasteigenvalueofG.Inthispaper,weshowthat,ifGisconnectedbutnotcomplete,thenλn（G）≤λn(Kn-11)andtheequalityholdsifandonlyifGKn-11,whereKn-11,isthegraphobtainedbythecoalescenceofacompletegraphKn-1ofn-1verticeswithapathP2oflengthoneofitsvertices.

简介：Wepresentnewsufficientconditionsonthesolvabilityandnumericalmethodsforthefollowingmultiplicativeinverseeigenvalueproblem:Givenann×nrealmatrixAandnrealnumbersλ1,λ2,...,λn,findnrealnumbersc1,c2,...,cnsuchthatthematrixdiag(c1,c2,...,cn)Ahaseigenvaluesλ1,λ2,...,λn.

简介：Cheng类型不平等，Cheeger类型不平等和Faber-Krahn-type不平等被概括到Finslermanifolds。为一个协议，与加权的Ricci弯曲歧管的Finsler从在下面跳了由一个否定常数，第一个特征值的Li-Yaus评价也被给。

简介：isgainedbydeletingthekthrowandthekthcolumn（k=1,2,...,n）fromTn.Weputfor-wardaninverseeigenvalueproblemtobethat:Ifwedon’tknowthematrixT1,n,butweknowalleigenvaluesofmatrixT1,k-1,alleigenvaluesofmatrixTk+1,k,andalleigenvaluesofmatrixT1,ncouldweconstructthematrixT1,n.Letμ1,μ2,…,μk-1,μk,μk+1,…,μn-1,

简介：LetT1,nbeann×nunreducedsymmetrictridiagonalmatrixwitheigenvaluesλ1

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简介：Derivativesofeigenvaluesandeigenvectorswithrespecttoparametersinsymmetricquadraticeigenvalueproblemarestudied.Thefirstandsecondorderderivativesofeigenpairsaregiven.Thederivativesarecalculatedintermsoftheeigenvaluesandeigenvectorsofthequadraticeigenvalueproblem,andtheuseofstatespacerepresentationisavoided,hencethecostofcomputationisgreatlyreduced.Theefficiencyofthepresentedmethodisdemonstratedbyconsideringaspring-mass-dampersystem.

简介：一张签署的图是一张图，一个符号属于每个边。这篇论文从图扩大拉普拉斯算符矩阵的一些基本概念到签署的图。Inparticular，在最少的拉普拉斯算符特征值之间的关系和一张签署的图的失衡的海角被调查。

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简介：Acouplingmethodoffiniteelementandinfinitelargeelementisproposedforthenumericalsolutionofaneigenvalueprobleminunboundeddomainsinthispaper.Withsomeconditionssatisfied,theconsideredproblemisprovedtohavediscretespectra.Severalnumericalexperimentsarepresented.Theresultsdemonstratethefeasibilityoftheproposedmethod.

简介：LetH∈Cn×nbeann×nunitaryupperHessenbergmatrixwhosesubdiagonalelementsareallpositive.PartitionHasH=[H11H12H21H22],(0.1)whereH11isitsk×kleadingprincipalsubmatrix;H22isthecomplementarymatrixofH11.Inthispaper,Hisconstructeduniquelywhenitseigenvaluesandtheeigenvaluesof(H|^)11and(H|^)22areknown.Here(H|^)11and(H|^)22arerank-onemodificationsofH11andH22respectively.

简介：Applyingconstructedhomotopyanditsproperties,wegelsomesufficientconditionsforthesolvabilityofalgebraicinverseeigenvalueproblems,whicharebetterthanthatofthepaper[4]insomecases.Inverseeigenvalueproblems,solvability,sufficientconditions.

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简介：Atwo-leveldiscretizationmethodforeigenvalueproblemsisstudied.ComparedtothestandardGalerkinfiniteelementdiscretizationtechniqueperformedonafinegridthismethoddiscretizestheeigenvalueproblemonacoarsegridandobtainsanimprovedeigenvector(eigenvalue)approximationbysolvingonlyalinearproblemonthefinegrid(ortwolinearproblemsforthecaseofeigenvalueapproximationofnonsymmetricproblems).TheimprovedsolutionhastheasymptoticaccuracyoftheGalerkindiscretizationsolution.ThelinkbetweenthemethodandtheiteratedGalerkinmethodisestablished.Errorestimatesforthegeneralnonsymmetriccasearederived.

简介：LetG=(V(G),E(G))beasimpleconnectedgraphofordern.Foranyverticesu,v,w∈V(G)withuv∈E(G)anduw∈E(G),anedge-rotatingofGmeansrotatingtheedgeuv(aroundu)tothenon-edgepositionuw.Inthiswork,weconsiderhowtheleasteigenvalueofagraphperturbswhenthegraphisperformedbyrotatinganedgefromtheshorterhangingpathtothelongerone.

简介：AbstractSomenewlocalandparallelfiniteelementalgorithmsareproposedandanalyzedinthispaperforeigenvalueproblems.Withthesealgorithms,thesolutionofaneigenvalueproblemonafinegridisreducedtothesolutionofaneigenvalueproblemonarelativelycoarsegridtogetherwithsolutionsofsomelinearalgebraicsystemsonfinegridbyusingsomelocalandparallelprocedure.Atheoreticaltoolforanalyzingthesealgorithmsissomelocalerrorestimatethatisalsoobtainedinthispaperforfiniteelementapproximationsofeigenvectorsongeneralshape-regulargrids.

简介：1IntroductionLetRn×nbethesetofalln×nrealmatrices.Rn=Rn×1.Cn×ndenotesthesetofalln×ncomplexmatrices.Weareinterestedinsolvingthefollowinginverseeigenvalueprob-lems:ProblemA（Additiveinverseeigenvalueproblem）Givenann×nrealmatrixA=(aij),andndistinctrealnumbersλ1,λ2,…,λn,findarealn×ndiagonalmatrixD=diag

简介：Inthispapertheunsolvabilityofgeneralizedinverseeigenvalueproblemsalmosteverywhereisdiscussed.Wefirstgivethedefinitionsfortheunsolvabilityofgeneralizedinverseeigenvalueproblemsalmosteverywhere.Thenadoptingthemethodusedin[14],wepresentsomesufficientconditionssuchthatthegeneralizedinverseeigenvalueproblemsareunsohablealmosteverywhere.

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简介：Nonlinearrank-onemodificationofthesymmetriceigenvalueproblemarisesfromeigen-vibrationsofmechanicalstructureswithelasticallyattachedloadsandcalculationofthepropagationmodesinopticalfiber.Inthispaper,wefirststudytheexistenceanduniquenessofeigenvalues,andtheninvestigatethreenumericalalgorithms,namelyPicarditeration,nonlinearRayleighquotientiterationandsuccessivelinearapproximationmethod(SLAM).TheglobalconvergenceoftheSLAMisprovenundersomemildassumptions.NumericalexamplesillustratethattheSLAMisthemostrobustmethod.