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：Forasubdivision△ofaregionind-dimensionalEuclideanspace.weconsidercomputationofdimensionandofbasisfunctioninsplinespaceS((△)consistingofallCpiecewisePolynomialfunc-tionsover△ofdegreeatmostk.AcomputationalschemeispresentedforcomputingthedimensionandbasesofsplinespaceS(△).ThisschemebasedOntheGrobnerbasisalgorithmandthesmoothco-factormethodforcomputingmultivariatespline.Forbivariatesplines,explicitbasisfunctionsofS(△)ageobtainedforanyintegerkandrwhen△isacross-cutpartition.

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简介：ThemultivariatesplineswhichwerefirstpresentedbydeBooorasacompletetheoreticalsystemhaveintriguedmanymathematicianswhohavedevotedmanyworksinthisfieldwhichisstillintheprocessofdevelopment.Theauthorofthispaperisinterestedintheareaofinter-polationwithspecialemphasisontheinterpolationmethodsandtheirapproximationorders.ButsuchB-splines(bothunivariateandmultivariate)donotinterpolateddirectly,soIap-proachedthisprobleminanotherwaywhichistoextendmyinterpolatingsplineofdegree2n-1inunivariatecase(See[7])tomultivariatecase.Iselectedtriangulatedregionwhichisinspiredbyothermathematicians’works(e.g.[2]and[3])andextendtheinterpolatingpolynomialsfromunivariatetom-variatecase(See[10])Inthispapersomeresultsinthecasem=2arediscussedandprovedinmoreconcretedetails.Basedonthesepolynomials,theinterpolatingsplines(itisdefinedbymeaspiecewisepolynomialsinwhichtheunknownpar-tialderivativesaredeterminedundercertaincontinuousconditions)arealsodiscussed.Theapproximationordersofinterpolatingpolynomialsandofcubicinterpolatingsplinesareinverstigated.Welunitedourdiscussionontherectangulardomainwhichispartitionedintoequalrighttriangles.Astothecaseinwhichtherectangulardomainispartitionedintounequalrighttrianglesaswellasthecaseofmorecomplicateddomains,wewilldiscussinthenextpa-per.

简介：ThepaperconsiderstheKrylov-LanczosandtheEckhoffapproximationsforrecoveringabivariatefunctionusinglimitednumberofitsFouriercoefficients.Theseapproximationsarebasedoncertaincorrectionsassociatedwithjumpsinthepartialderivativesoftheapproximatedfunction.ApproximationoftheexactjumpsisaccomplishedbysolutionofsystemsoflinearequationsalongtheideaofEckhoff.AsymptoticbehaviorsoftheapproximatejumpsandtheEckhoffapproximationarestudied.Exactconstantsoftheasymptoticerrorsarecomputed.Numericalexperimentsvalidatetheoreticalinvestigations.

简介：InthispaperweusethesimplexB-splinerepresentationofpolynomialsorpiecewisepolynomialsintermsoftheirpolarformstoconstructseveraldifferentialordiscretebivariatequasiinterpolantswhichhaveanoptimalapproximationorder.Thismethodprovidesanefficienttoolfordescribingmanyapproximationschemesinvolvingvaluesand(or)derivativesofagivenfunction.

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简介：Extendingtheresultsof[4]intheunivariatecase,inthispaperweprovethatthebivariateinterpolationpolynomialsofHermite-FejerbasedontheChebyshevnodesofthefirstkind,thoseofLagrangebasedontheChebyshevnodesofsecondkindand±1,andthoseofbivariateShepardoperators,havethepropertyofpartialpreservationofglobalsmoothness,withrespecttovariousbivariatemoduliofcontinuity.

简介：FormeasurablefunctionsfoftworealvariablesthereareconsideredtheBiikeansumsL_m,n∫ofparametricextensionsofcertainunivariateDurrmerer-ivpeoperulors

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简介：Thispaperanalysesthelocalbehaviorofthesimpleoff-diagonalbivariatequadraticfunctionapproximationtoabivariatefunctionwhichhasagivenpowerseriesexpansionabouttheorigin.Itisshownthatthesimpleoff-diagonalbivariatequadraticHermite-Padéformalwaysdefinesabivariatequadraticfunctionandthatthisfunctionisanalyticinaneighbourhoodoftheorigin.NumericalexamplescomparetheobtainedresultswiththeapproximationpowerofdiagonalChisholmapproximantandTaylorpolynomialapproximant.

简介：BymakinguseofThiele-typebivariatebranchedcontinuedfractionsandSumelsoninverse,weconstructafewkindsofbivariatevectorvaluedrationalinterpolonts(BVRIs)overrectangulargridsandfindoutcertainrelationsamongtheseBVRIssuchasboundaryidentityandduality.

简介：Inthispaper,weproposeamethodtodealwithnumericalintegralbyusingtwokindsofC~2quasi-interpolationoperatorsonthebivariatesplinespace,andalsodis-cusstheconvergencepropertiesanderrorestimates.Moreover,theproposedmethodisappliedtothenumericalevaluationof2-Dsingularintegrals.Numericalexper-imentswillbecarriedoutandtheresultswillbecomparedwithsomepreviouslypublishedresults.

简介：1IutroductionManykindsofmatrix-valuedrationalinterpolationorapproximationproblemshaveappearedinrecentyears([1-7]).MotivatedbyGraves-Morris’Thiele-typevector-val-uedrationalinterpolants[6],GuChuanqingandChenZhibing[7]discussedthematrix-valuedrationalinterpolantsinThiele-typecontinuedfractionform,withmatrix-valuednu-

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简介：BoththeexpansiveNewton'sinterpolatingpolynomialandtheThiele-Werner'sin-terpolationareusedtoconstructakindofbivariateblendingThiele-Werner'soscula-toryrationalinterpolation.Arecursivealgorithmanditscharacteristicpropertiesaregiven.Anerrorestimationisobtainedandanumericalexampleisillustrated.

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简介：Inthispaper,thefuzzyreliabilityfunctionZ=X+Yhasbeenderived.InthecaseofthatX,YsubjectstoMarshall-Olkinbivariateexponentialdistribution,assumingμ=μ1μ2.

简介：Thispaperconstructsanewkindofblockbasedbivariateblendingrationalinterpolationviasymmetricbranchedcontinuedfractions.Theconstructionprocessmaybeoutlinedasfollows.Thefirststepistodividetheoriginalsetofsupportpointsintosomesubsets(blocks).Thenconstructeachblockbyusingsymmetricbranchedcontinuedfraction.FinallyassembletheseblocksbyNewton’smethodtoshapethewholeinterpolationscheme.OurnewmethodoffersmanyflexiblebivariateblendingrationalinterpolationschemeswhichincludetheclassicalbivariateNewton’spolynomialinterpolationandsymmetricbranchedcontinuedfractioninterpolationasitsspecialcases.Theblockbasedbivariateblendingrationalinterpolationisinfactakindoftradeoffbetweenthepurelylinearinterpolationandthepurelynonlinearinterpolation.Finally,numericalexamplesaregiventoshowtheeffectivenessoftheproposedmethod.