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简介：Inthisnotewepresentaconstructiveproofofsymmetricaldeterminantalformulasforthenumeratoranddenominatorofanordinaryrationalinterpolant,considertheconfluencecaseandgivenewdeterminantalformulasoftherationalinterpolantbymeansofLagrange’sbasisfunctions.

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简介：WestructureakindofrationalsplinesfarintroducingsomeofthePadeapproximenttechniquesintorationalsplines.Inthispaper,theresultsontheexistence,uniquenessandalgorithmoftherationalsplinearegivenandanumericalexampleisprovided.

简介：Thispaperdealswithrationalinterpolation.Fromalgebraicviewpoint,wepresentanalgebraicformulationofrationalinterpolationanddiscusstheexistenceoftheinterpolationfunction.Finallyanalgorithmforunivariatecaseandanexamplearepresented.

简介：Asweknow,Newton'sinterpolationpolynomialisbasedondivideddiffer-enceswhichcanbecalculatedrecursivelybythedivided-differenceschemewhileThiele'sinterpolatingcontinuedfractionsaregearedtowardsdeterminingarationalfunctionwhichcanalsobecalculatedrecursivelybyso-calledinversedifferences.Inthispaper,bothNewton'sinterpolationpolynomialandThiele'sinterpolatingcontinuedfractionsareincorporatedtoyieldakindofbivariatevectorvaluedblendingrationalinterpolantsbymeansoftheSamelsoninverse.Blendingdifferencesareintroducedtocalculatetheblendingrationalinterpolantsrecursively,algorithmandmatrix-valuedcasearedis-cussedandanumericalexampleisgiventoillustratetheefficiencyofthealgorithm.

简介：Afamilyofpiecewiserationalquinticinterpolationispresented.Eachinterpolationofthefamily,whichisidentifieduniquelybythevalueofaparameterαi,isofC2continuitywithoutsolvingasystemofconsistencyequationsforthederivativevaluesattheknots,andcanbeexpressedbythebasisfunctions.InterpolantisofO(hr)accuracywhenf(x)?Cr[a,b],andtheerrorshaveonlyasmallfloatingforabigchangeoftheparameterαi,itmeanstheinterpolationisstablefortheparameter.Theinterpolationcanpreservetheshapepropertiesofthegivendata,suchasmonotonicityandconvexity,andaproperchoiceofparameterαiisgiven.

简介：Anrationalandeffectivefuzzychoicestrategytocompetitionandcooperation(C&C)fortwo-playercompetitivesituationsissubmittedinthispaper,whichcomputesplayer'stotalperformanceincludingbothabsoluteandrelativeperformanceandrepresentingtherelationbetweencooperationdegreeandtheobjectiveandsubjectivefactorsthattheyarefaced;analgorithmtothepracticalproblembasedonfuzzyoptimizingtechniqueisthenanalyzedstressinthefuzzysense,themethodcanbeusedfortheplayertoobtainarationalbehaviourunderthecompetitiveenvironment,somekeyfactorsforimplementationthedecisionmakingschemeareproposedtoo;finally,thesuggestedmethodisillustratedbyanumericalexample.Itprovidesusefulreferencemodelfortheplayertorealizerationaldecisionmakingstrategyundertheunceratintyenvironment.

简介：AnorthogonalsystemofrationalfunctionsisderivedfromthemappedLaguerrepolynomials,whichisusedfornumericalsolutionofsingulardifferentialequations.Amodelproblemisconsidered.Amultiple-stepalgorithmisdevelopedtoimplementthismethod.Numericalresultsshowtheefficiencyofthisnewapproach.

简介：在这篇论文，我们学习随它的合理翻译设置的Mcmullen的交叉。主要困难是交叉的产生结构。由翻译向量的根值扩大，我们给它的分数维的描述。我们发现这些的Hausdorff措施给形式价值其非零仅仅来自翻译向量的一个分离系列(x，y)与它的根值扩大。

简介：Thispaperstudiesthedynamicsoftheanalyticfamilyz+1/z+banddescribesthetopologyoftheparameterspace,structuralstabilityandJ-stability.Themappingclassgroupofalmostallmapsoftheabovefamilyisdetermined.

简介：FromthesurveyofcoastalresourcesandthefunctionalzoingofthemarineandcoastsalareasofShandongProvince,theauthorshavecollectedagooddeelofpracticaldata,andatthesametime,foundoutsomeirrationalphenomenaintheexploitationandutilizationofcoastalresources.TaKingthecoastalareaofShandongProvinceasanexample.Thispapermakesananalysisontherationalutilizationofcoastalresources.

简介：Efficientalgorithmsareestablishedforthecomputationofbivariatelacunaryvectorvaluedrationalinterpolantsbasedonthebranchedcontinuedfractionsandanumericalexampleisgiventoshowhowthealgorithmsareimplemented,

简介：In[3],akindofmatrix-valuedrationalinterpolants(MRIs)intheformofRn(x)=M(x)/D(x)withthedivisibilityconditionD(x)|‖M(x)‖2,wasdefined,andthecharacterizationtheoremanduniquenesstheoremforMRIswereproved.Howeverthisdivisibilityconditionisfoundnotnecessaryinsomecases.Inthispaper,weremovethisrestrictedcondition,definethegeneralizedmatrix-valuedrationalinterpolants(GMRIs)andestablishthecharacterizationtheoremanduniquenesstheoremforGMRIs.OnecanseethatthecharacterizationtheoremanduniquenesstheoremforMRIsarethespecialcasesofthoseforGMRIs.Moreover,bydefiningakindofinnerproduct,wesucceedinunifyingtheSamelsoninversesforavectorandamatrix.

简介：Avarietyofmatrixrationalinterpolationproblemsincludethepartialrealizationproblemformatrixpowerseriesandtheminimalrationalinterpolationproblemforgeneralmatrixfunctions.Severalproblemsincircuittheoryanddigitalfilterdesigncanalsobere-ducedtothesolutionofmatrixrationalinterpolationproblems[1—4].Bymeansofthereachabilityandtheobservabilityindicesofdefinedpairsofmatrices,Antoulas,Ball,KangandWillemssolvedtheminimalmatrixrationalinterpolationproblemin[1].Onthe

简介：在这篇论文，我们在一套部分微分合理参量的方程P的theimplicitization为下列问题建议算法。(1)发现一个特征为P的含蓄的主要理想设定；(2)为P的图象发现一个正规代表；(3)决定P的参数是否是独立的，并且如果不，tore-parameterizeP以便新参量的方程有独立参数；(4)P印射计算倒置，并且作为后果，决定P是否是合适的。

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简介：LetιbeatriangulationofapolygonaldomainDR2withverticesV={v1:1≤i≤N,}andRSk（D,τ）={u∈Ck（D）:(T∈τ,u|τisarationalfunction}.Thepurposeofthispaperistostudytheexist-enceandconstructionofC^{μ-rationalsplinefunctionsonanytriangulationτforCAGD.TheHermiteprob-lemHμ（V,U）={findu∈}

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简介：AnewkindofvectorvaluedrationalinterpolantsisestablishedbymeansofSamelsoninverse,withscalarnumeratorandvectorvalueddenominator.ItisessentiallydifferentfromthatofGraves-Morris(1983),wheretheinterpolantsareconstructedbyThiele-typecontinuedfractionswithvectorvaluednumeratorandscalardenominator.Thenewapproachismoresuitabletocalculatethevalueofavectorvaluedfunctionforagivenpoint.Andanerrorformulaisalsogivenandproven.