非收縮三角剖分下二元樣條函數(shù)空間的維數(shù).pdf

1、廣西民族大學(xué)碩士學(xué)位論文非收縮三角剖分下二元樣條函數(shù)空間的維數(shù)姓名：衣娜申請(qǐng)學(xué)位級(jí)別：碩士專業(yè)：計(jì)算數(shù)學(xué)指導(dǎo)教師：劉煥文20080401DIMENSIONSOFBIVARIATESPLINESPACESOVERUNCONSTRICTEDTRIANGULATIONSABSTRACTThebivariatesplinespacesSrn(?)onregulartriangulationshaveverypopularuseinmanyfie

2、lds.Therefeitsdimensionproblemhasbeencontinuouslyconcernedbythemathematicscomputerscholars.HoweveritisfoundthatthedimensionsofSrn(?)dependnotonlyonthetopologicalpropertiesoftriangulationsbutalsoonthegeometricshape.Thisma

3、kesitdifficulttodetermihedimensions.Fthegeneralregulartriangulationswhenn≥3r2n=4r=1theproblemofdimensionshasbeensolved.InthispaperwefocusontheproblemofdimensionsofsplinefunctionspaceSrn(?)undertheunconstrictedtriangulati

4、onsgeneralizedunconstrictedtriangulations.Thecontentsarearrangedasfollows.FirstthedimensionsofbivariatesplinefunctionspacesSrn(?)underaclassofspecialtriangulations–unconstrictedtriangulationsareachievedbystudyingthedistr

5、ibutionofminimaldeterminingsetonstartyperegional.Thenbyintroducingtwonewoperatsintriangulationconstructionakindofgeneralizedunconstrictedtriangulationisdefinedwhichisanexpansionoftheunconstrictedtriangulationsintroducedb

6、yFarinin2006.ItcontainssomewellknowntriangulationssuchastheMganScotttheRobbinstriangulationsonwhichthedimensionproblemsaredifficulttobesolved.thenthedimensionsofbivariateC1cubicsplinespacesovergeneralizedunconstrictedtri