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简介：InthispaperitisstudiedthatthegeneratedtheoryofwaverecursiveinterpolationofuniformT-subdivi-stonschemeincludewaveparameter.ThepaperanalysestheconvergenceofsequencesofcontrolpolygonsproducedbywaverecursiveinterpolationT-subdivisionschemeoftheformj=l,2,…,T-1;m=O,l,…,nTk;k=0,l,2,…,anddifferentiabilityofthelimitcurve.

简介：Inthispaper,amethodtoconstructasurfacewithpointinterpolationandnormalinterpolationispresented.Analgorithmtoconstructthediscreteinterpolationisalsopresented,whichhasthetimecomplexityO(NlogN),whereNinthenumberofscatteredpoints.

简介：ThispaperintroducesthedefinitionoftheOrthogonalTypeNodeConfigurationanddiscussesthecorrespondingmultivariateLagrange,HermiteandBirkhoffinterpolationproblemsinhighdimensionalspaceRs(s＞2).ThisnodeconfigurationcanbeconsideredtobeakindofextensionoftheCrossTypeNodeConfiguration[1],[2]inR2tohighdimensionalspaces.AndtheMixedTypeNodeConfigurationinRs(s＞2)isalsodiscussedinthispaperinanexample.

简介：Theobjectinthispaperistoconsidertheproblemofexistence,uniqueness,explicilrepresentationof（0,2）-interpolationonthezerosof（1-x2）P_{n-1（x）/xwhennisodd,wherePn-1denotesLegendrepolynomialofdegreen-1,andtheproblemofconvergenceofinterpolatorypolynomials.}

简介：Thispaperdealswithrationalinterpolation.Fromalgebraicviewpoint,wepresentanalgebraicformulationofrationalinterpolationanddiscusstheexistenceoftheinterpolationfunction.Finallyanalgorithmforunivariatecaseandanexamplearepresented.

简介：Thef(x)∈C[-1,1]isgiven,amodificationisgiventotheinterpolationpolynomialQn(f;x)(thepower,lessthanλn,1

简介：LetS∞denotetheunitsphereinsomeinfinitedimensionalcomplexHilbertspace(H,<·,·>)Letz1,z2,…,z1bedistinctpointsonS∞Thispaperdealswithinterpolationofarbitrarydataonthezjbyafunctioninthelinearspanofthelfunctionswhenisasuitablefunctionthatoperatesonnonnegativedefinitematrices.Conditionsforthestrictpositivedefinitenessofthekernelareobtained.

简介：Forgivendata,aninterpotantissought,sothatacerlaintconvcxfunctionaldefinedbvaYoung’sfunctioninthecorrespondingOrliczspaceisminuimized.Thefeedciamoregeneralkindofspacescanbeusedforselectingtheinterpoluntsinanudequareclassoffunctiois.

简介：在二维的空间R2的bivariate插值在一维的空间R是比那更复杂的，因为没有在R2的连续功能的Haar空间。因此，bivariate插值没为一套任意的不同pairwise点有一个唯一的答案。在这个工作，我们建议取决于点的基础的一种类型以便bivariate插值为不同pairwise点的任何集合有唯一的答案。在这种情况中，bivariate插值的矩阵把半继承因式分解。

简介：Forgivendata(ti,yi),I=0,1,…,n,0=t0＜t1＜…＜tn=1westudyconstrainedinterpolationproblemofFavardtypeinf{‖f'‖∞|f∈W2∞[0,1],f(ti)=yi,i=0,…,n,l(f;[0,1])≤l0},wherel(f';[0,1])=∫10/1+f'2(x)dxisthearclengthoffin[0,1].Weprovetheexistenceofasolutionf*oftheaboveproblem,thatisaquadraticsplinewithasecondderivativef'*,whichcoincideswithoneoftheconstants-‖f'*‖∞,0,‖f'*‖∞betweeneverytwoconsecutiveknots.Thus,weextendaresultofKarlinconcerningFavardproblem,tothecaseofrestrictedlengthinterpolation.

简介：SeveralcubatureformulasonthecubicdomainsarederivedusingthediscreteFourieranalysisassociatedwithlatticetiling,asdevelopedin[10].ThemainresultsconsistofanewderivationoftheGaussiantypecubaturefortheproductChebyshevweightfunctionsandassociatedinterpolationpolynomialson[-1,1]~2,aswellasnewresultson[-1,1]~3.Inparticular,compactformulasforthefundamentalinterpolationpolynomialsarederived,basedonn~3/4+(?)(n~2)nodesofacubatureformulaon[-1,1]~3.

简介：Theobjectiveofthispaperistogiveaconstructiveapproachtothesolutionofthefundamentalfunctionsforcardinalinterpolationfromashift-invariantspacegeneratedbythe(multi-)integertranslatesofsomecompactlysupportedfunctionwhosepolynomialsymbolhasanon-emptyzeroset.ThisproblemwasfirstintroducedbyChut,Diamond,andRaphael,whereexplicitsolutionsweregivenforvariouszerosets.Later,deBoor,Hollig,andRiemenschneidergaveanexistenceproofforzerosetswhicharemoregeneral.Inthispa-per,wegiveanintegralrepresentationofthefundamentalsolutionsthatcanbemadeexplicitinsomecasesandwewillalsogiveagrowthconditionofsuchfundamentalsolutions.Thefour-directionalboxsplineswillbeusedasanillustrativeexample.

简介：让功能f∈C[1，1]，在有限收集Y:=改变它的monotonisity{y1，...，ys}s点yi∈(1，1)。为每n≥N(Y)，我们构造代数学的多项式Pn，度≤n，它是有f的comonotone，那是它在一样的monotonisity削尖的变化yi作为f，；

简介：Theregularizedimageinterpolationmethodiswidelyusedbasedonthevectorinterpolationmodelinwhichdown-samplingmatrixhasverylargedimensionandneedslargestorageconsumptionandhighercomputationcomplexity.Inthispaper,afastalgorithmforimageinterpolationbasedonthetensorproductofmatricesispresented,whichtransformsthevectorinterpolationmodeltomatrixform.Theproposedalgorithmcanextremelyreducethestoragerequirementandtimeconsumption.Thesimulationresultsverifytheirvalidity.

简介：BytheweakatomicdecompositionsofweakmartingaleHardyspaces,weinvestigatetheinterpolationspacesbetweenweakmartingaleHardyspacesandmartingaleHardyspaces.

简介：在为给定的域Rn的锥性质的唯一的假设下面，这被证明为在Sobolev空格Wm的函数的中间的衍生物的插值不平等，p()或甚至在某加权的Sobolve空格Wwm，p()仍然成立。也就是说，被跳或让一致的锥性质的平常的另外的限制两个都被移开。使用的主要工具是多项式不平等，它由是为光滑、分析的功能的也获得的pointwise版本插值不平等。如此的pointwise版本不平等在有锥性质的无界的领域在无穷为衍生物给明确的腐烂估计。作为腐烂估计的应用，光滑的功能的光线的基础功能近似上的以前的结果被扩大到衍生物同时的近似。

简介：ItisaclassicalresultofBernsteinthatthesequenceofLagrangeinterpolationpolynomialsto|x|atequallyspacednodesin[-1,1]divergeseverywhere,exceptatzeroandtheend-points.InthispaperweshowthatthesequenceofLagrangeinterpolationpolynomialscorrespondingtothefunctionswhichpossessbettersmoothnessonequidistantnodesin[-1,1]stilldivergeseverywhereintheintervalexceptatzeroandtheend-points.

简介：ReconstructinganHR(high-resolution)imagewhichpreservestheimageintrinsicstructuresfromitsLR(low-resolution)counterpartishighlychallenging.Thispaperproposesanewsurfacereconstructionalgorithmappliedtoimageinterpolation.Theinterpolationsurfaceforthewholeimageisgeneratedbyputtingallthequadraticpolynomialpatchestogether.Inordertoeliminatethejaggiesoftheedge,anewweightfunctioncontainingedgeinformationisincorporatedintothepatchreconstructionprocedureasaconstraint.Extensiveexperimentalresultsdemonstratethatourmethodproducesbetterresultsacrossawiderangeofscenesintermsofbothquantitativeevaluationandsubjectivevisualquality.

简介：Letφbeanormalfunctionon[0,1]andA~1(φ)theBergmanspacewithweightφ(|z|)/(1-|z|~2).AnatomicdecompositiontheoremforA~1(φ)isobtained,andanecessaryandnearly-sufficientconditionisgiventomakeasequenceofpointsinterpolateforA~1(φ).