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简介：Wepresentaclassofasymptoticallyoptimalsuccessiveoverrelaxationmethodsforsolvingthelargesparsesystemoflinearequations.Numericalcomputationsshowthatthesenewmethodsaremoreefficientandrobustthantheclassicalsuccessiveoverrelaxationmethod.

简介：我们给一般表情，分析代数学的性质并且导出为与微分操作员的各种各样的订单的正弦discretizations联系的Toeplitz矩阵的一个序列的特征值界限。我们证明这些Toeplitz矩阵能是令人满意地由通过证明preconditioned矩阵的系列一致地被围住的某些bandedToeplitz矩阵的preconditioned。特别地，我们也为bandedToeplitzpreconditioners导出特征值界限。这些结果在为从平常、部分的微分方程的正弦discretizations产生的线性方程的系统构造高质量的结构化的preconditioners是基本的，并且在为相应preconditioned矩阵分析代数学的性质和发源特征值界限是有用的。数字例子被给显示出bandedToeplitzpreconditioners的有效性。

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简介：几个Galerkin-Petrov方法，包括的多项式搭配和分析元素的集中在Dirichlet空间的Toeplitz操作员的搭配方法，被建立。特别地，如果基础和测试功能拥有某些圆形的对称，如此的方法收敛，这被显示出。给词调音：GalerkinPetrov方法；多项式搭配；分析元素搭配；Toeplitz操作员；Dirichlet空间

简介：Inthispaperaclassoftheextendedsecondderivativeformulasispresented.Basedontheextendedk-stepsecondderivativeformulaanewpredictor-correctormethodcalledExtendedk-stepsecondDerivativeMethodforstiffsystemsisformulatedwiththek-stepsecondderivativeformulaasitsimplicitpredictor.Theextendedsecondderivativemethodshavethehigherordersandthebetterstabilityproperties.Thecomputationaleffortiscomparitivelylarge,butmuchofitcanbesaved,sothatthemethodsareacceptableandefficient.

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简介：Undersuitableconditions,themonotoneconvergenceabouttheprojectediterationmethodforsolvinglinearcomplementarityproblemisprovedandtheinfluenceoftheinvolvedparametermatrixontheconvergencerateofthismethodisinvestigated.

简介：Somespecificnon-isotropicJacobiapproximationsinmultiple-dimensionsareinvestigated,whichareusedfornumericalsolutionsofdifferentialequationsonvariousunboundeddomains.Theconvergenceofproposedschemesareproved.Someefficientalgorithmsareprovided.Numericalresultsarepresentedtoillustratetheefficiencyofthisnewapproach.

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简介：Inthispaper,wedealwiththeboundednessandtheasymptoticstabilityoflinearandone-legmultistepmethodsforgeneralizedpantographequationsofneutraltype,whicharisefromsomefieldsofengineering.Somecriteriaoftheboundednessandtheasymptoticstabilityforthemethodsareobtained.

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简介：Lookbackoptionsarepath-dependentoptions.Ingeneral,thebinomialtreemethods,asthemostpopularapproachestopricingoptions,involveapathdependentvariableaswellastheunderlyingassetpriceforlookbackoptions.However,forfloatingstrikelookbackoptions,asingle-statevariablebinomialtreemethodcanbeconstructed.Thispaperisdevotedtotheconvergenceanalysisofthesingle-statebinomialtreemethodsbothfordiscretelyandcontinuouslymonitoredAmericanfloatingstrikelookbackoptions.Wealsoinvestigatesomepropertiesofsuchoptions,includingeffectsofexpirationdate,interestrateanddividendyieldonoptionsprices,propertiesofoptimalexerciseboundariesandsoon.

简介：TheconvergenceoftheparallelmatrixmultisplittingrelaxationmethodspresentedbyWang(LinearAlgebraandItsApplications154/156(1991)473-486)isfurtherinvestigated.Theinvestigationsshowthattheserelaxationmethodsreallyhaveconsiderablylargerconvergencedomains.

简介：1.IntroductionThediscretizationofmanysecondorderselfadjointellipticboundaryvalueproblemsbythefiniteelementmethodleadstolargesparsesystemsoflinearequationswithsymmetricpositivedefinite(SPD)coefficientmatrices.Fortheselinearsystems,algebraicmultilevelp...

简介：Thispaperdealswiththenumericalsolutionofinitialvalueproblemsforsystemsofdifferentialequationswithadelayargument.Thenumericalstabilityofalinearmultistepmethodisinvestigatedbyanalysingthesolutionofthelestequationy’(t)=Ay(t)+By(1-t),whereA,BdenoteconstantcomplexN×N-matrices,andt>0.Weinvestigatecarefullythecharacterizationofthestabilityregion.

简介：ThevalueofaEuropeanoptionsatisfiestheBlack-Scholesequationwithappropriatelyspecifiedfinalandboundaryconditions.Wetransformtheproblemtoaninitialboundaryvalueproblemindimensionlessform.Therearetwoparametersinthecoefficientsoftheresultinglinearparabolicpartialdifferentialequation.Forarangeofvaluesoftheseparameters,thesolutionoftheproblemhasaboundaryoraninitiallayer.Theinitialfunctionhasadiscontinuityinthefirst-orderderivative,whichleadstotheappearanceofaninteriorlayer.Weconstructanalyticallytheasymptoticsolutionoftheequationinafinitedomain.Basedontheasymptoticsolutionwecandeterminethesizeoftheartificialboundarysuchthattherequiredsolutioninafinitedomaininxandatthefinaltimeisnotaffectedbytheboundary.Also,westudycomputationallythebehaviourinthemaximumnormoftheerrorsinnumericalsolutionsincasessuchthatoneoftheparametersvariesfromfinite(orprettylarge)tosmallvalues,whiletheotherparameterisfixedandtakeseitherfinite(orprettylarge)orsmallvalues.Crank-Nicolsonexplicitandimplicitschemesusingcenteredorupwindapproximationstothederivativearestudied.Wepresentnumericalcomputations,whichdetermineexperimentallytheparameter-uniformratesofconvergence.Wenotethatthisrateisratherweak,dueprobablytomixedsourcesoferrorsuchasinitialandboundarylayersandthediscontinuityinthederivativeofthesolution.

简介：Thispaperconsiderstheasymptoticstabilityanalysisofbothexactandnumericalsolutionsofthefollowingneutraldelaydifferentialequationwithpantographdelay.{x′(t)+Bxd(t)+Cx′(qt)+Dx(qt)=0,t>0,x(0)=X0,}whereB,C,D∈C^d×d,q∈(0,1),andBisregular.Aftertransformingtheaboveequationtonon-automaticneutralequationwithconstantdelay,wedeterminesufficientconditionsfortheasymptoticstabilityofthezerosolution.Furthermore,wefocusontheasymptoticstabilitybehaviorofRunge-Kuttamethodwithvariablestepsize.ItisprovedthataLstableRunge-Kuttamethodcanpreservetheabove-mentionedstabilityproperties.

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