二元樣條函數(shù)空間及弱樣條函數(shù)空間的維數(shù).pdf

1、廣西民族大學碩士學位論文二元樣條函數(shù)空間及弱樣條函數(shù)空間的維數(shù)姓名：王偉申請學位級別：碩士專業(yè)：計算數(shù)學指導教師：劉煥文20090401DIMENSIoNSoFBIVARIATESPLINESPACESANDBIVARIATEWEAKSPLINESPACESABSTRACTAbivariatesplinespaces3(a)definedonatriangulation△ofaplanarpolygonalregionisasetcon

2、sistingofpiecewisepolynomialswithdegreedandglobalCrsmoothness，whichhasbeenwidelyappliedtOmanyfields，suchastheapproximationtheorythecomputeraidedgeometrydesign(CAGD)，waveletsandfiniteelementsThemostimportantproblemaboutth

3、esplinespacesistOdeterminetheirdimensionsGenerally，△isrestrictedtObearegulartriangulationweconsidertOde—terminethedimensionsofbivariatesplinespacesoverakindofspecialregulartriangulationsSpecificallyspeaking，akindofSO—cal

4、lednon—strictlydegeneratetriangulationswithdegree2isfirstlydefined，whichincludesmanywellknownrefinedtriangulationsasitsspecialcases，suchastheCloughTocherrefinedtriangulationACT，thetype1Powell—SabinrefinedtriangulationAPS

5、1，metype一2Powell—SabinrefinedtriangulationAPS2，theWangrefinedtriangulationAwandthetriangulatedquadrangulation◆thenthedimensionofbivariatesplinespaceS；(△)isgiven，whichisanextensionofAIfeldandSchumaker’Sdimensionalresultov

6、ernon—degeneratetriangulationsBesidesthegeneralsplinespaces，bivariateweaksplinespacesarealsousefulintheCAGD，HermitinterpolationsandfiniteelementsInthesecondpartinthisthesis，weturntOstudythedimensionofthesekindofweaksplin

7、espacesdefinedonappointedpointtriangulationsassociatedtoregulartriangulationsFirst，byusingtheB百ziernetmethodandthetechniqueofminimaldeterminingsets，thedimensionofbivariateweaksplinespace哎(IIA)withk=2uisdetermined，whereth

8、etriangulationAisanunionofaseriesofstarregions，ie，△=Ustar(vi)，andllAmeanstheappointedpointtriangulationwithonepointintheinteriorofeachedgeThisresultimprovesXuandWang’Sworkfromthecasek和tOthecasek≥2uSecond，thedimensionofbi