關(guān)于多元分次插值適定性問題的研究.pdf

1、遼寧師范大學(xué)碩士學(xué)位論文關(guān)于多元分次插值適定性問題的研究姓名：姜志敏申請學(xué)位級別：碩士專業(yè)：應(yīng)用數(shù)學(xué)指導(dǎo)教師：崔利宏20090501AbstractContent：MultivariateinterpolationisaclassicalandcomplicatedmathematicalproblemRecentyearspeoplehavecometofocusonmultivariateinterpolationespeciall

2、yonmultivariategradedinterpolationThereasonisthatmultivariateinterpolationhasawidespreadapplicationinmanyfields，suchasneuralnetworktechnologygeologicalsimulationandweatherforecastSotheproblemisresearchedfurtherinthispape

3、rAndthepoisednessofsetofnodesisdescribedbyalgebraicgeometrytheoryThepaperiscomposedoffourcharptersInthefirstcharpterweintroducethebasictheoryofmultivariatepolynomialinterpolationandrecentproductionInthesecondcharpter，usi

4、ngtheresultsofvarietyinalgebraicgeometrywegiveGr6bnerBases’methodandinterpolationinalgebraicmanifoldInthethirdcharpter，OnthebasicofbivariateLagrangeinterpolationalonganalgebraiccurvewithoutmultiplefactors，wegiveakindofme

5、thodofconstructingproperlyposedsetofnodesformultivariateLagrangeinterpolationinR3Inthefourchapter，wemainlydealwiththepoisednessofsetofnodesinmultivariategradedpolynomialinterpolationandgivenewconstrucotivemethodsofproper

6、lyposedsetofnodesinbivariategradedinterpolation，ie，Line—SuperpositionProcessandConicSuperpositionProcessAlsoweproveitreasonablebyexampleKeyWords：MultivariateGradedInterpolation；AlgebraicCurveAndSurface；GrSbnerBases；Algeb