一类特殊剖分上二元样条空间维数的奇异性分析

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1、一类特殊剖分上二元样条空间维数的奇异性分析OnsingularityofthedimensionsofthebivariatesplinespacesoveratypeofpartitionAbstractMultivariatesplinefunctionisanimportantresearchobjectinapproximationtheory,numericalanalysis，numericalsolutionsofdifferentialequations，etcandarewidelyap-pliedi

2、nengineering．Amultivariatesplinespaceisafinitedimensionallinearspace．Thedimensionofasplinespaceisimportantforthetheoriesandapplicationsonmultivariatesplines．However，thedimensionofasplinespaceissuchadifficultproblemthatwecanonlyobtainthedimensionalformulaeofsomes

3、pecialsplinespaces．Ingeneralcase，thedimensionformulaisunknown，especiallywhenthesplinespaceissingular．Inthisthesis，weutilizethesmoothingCofactor—conformalitymethodtodiscussthesingularitiesofbi—variatesplinespacesonsomepartitions，obtainsomenecessaryandsufficientco

4、nditionstothesingularitiesofthesesplinespaces．Inchapter1，webrieflyintroducesomebasictheoriesofmultivariatesplinesandtheSmoothingCofactor—Conformalitymethod，whichisthebasisofourfollowingwork．Inthefollowingchapters，weusethesmoothingCofactor—Conformalitymethodtores

5、earchonsingularitiesofbivariatesplinespacesoversomespecialpartitions．Inchapter2，weintroducesomebasicresultsofthedimensionsofsplinespaces．Firstly，wegivethedflnensionalformulaeofsplinespacesoncrosscutpartitionorquasi—crosscutpartitions．Secondly，wegivesomebasicresu

6、ltsoftriangulations，dimensionalformulaeofsplinespacesontriangulations．Finally，weintroducesomeresultsofthesingularityoftheMorgan—Scotttriangulationsandthestabilityofthedimensionsofgeneralsplinespaces．Inchapter3，weusethesmoothingCofactor—conformalitymethodtoanalyz

7、ethesplinespacesonapartitionofpolygon，obtainsomepropertiesofthesesplinespaceswhichareusefulltoresearchthesingularitiesofbivariatesplinespacesoversomeotherpartitions．Weobtainsomenecessaryandsufficientconditionstothesingularitiesofthesesplinespaces．Keywords：Multiv

8、ariatespline；SmoothingCofactor；SmoothingCofactor—Conformalitymethod；Dimension；Singularity—II大连理工大学硕士学位论文目录摘要⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯IAbstract⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯