多元Lagrange插值適定結(jié)點(diǎn)組及插值基的構(gòu)造.pdf

1、遼寧師范大學(xué)碩士學(xué)位論文多元Lagrange插值適定結(jié)點(diǎn)組及插值基的構(gòu)造姓名：張雙喜申請(qǐng)學(xué)位級(jí)別：碩士專(zhuān)業(yè)：應(yīng)用數(shù)學(xué)指導(dǎo)教師：崔利宏20070101AbstractContent：Polynomialinterpolationinseveralvariablesis8subjectwhichiscurrentlyanactiveareaofresearchFirst，weintroduceanddi日cu鶴thevmriou8metho

2、dsofmultivariatepolynomialinterpolationintheliteratureInparticular，usingthemultivariatedivideddifferenceintroducebYCdeBoor，weobtainaerrorformulafortensorproductinterpolationin時(shí)Multivariatepolynomialinterpolationisnotthe8

3、implegeneralizntionofunivariatecontextFirstofall，onemustsolvethewellpondproblemOneoftheworkisLiang’stheorem，whichtransferthebivariateLagTallgeinterpolationintoageometricalproblembymeausofalgebraicctLrVeSInchaptert11ree，w

4、edisctts8ChungandYadsGCconditionandimproveLiangstheoremFurthermore，usingtheresultofvarietyinalgebraicgeometrywestud)thegeometricalstructureofproperlyp∞edsetofnodes(PPSN)forinterpolationonalgebraichyperplane，andgiveaHyper

5、planeSuperpositionProcesstoconstructthePPSNforinterpolationonalgebraichyperplane，thereforewemakedearthegeometricalstructureofPPSNformultivariateLagrangeinterpolationThebasecalculatingmultivariateLagrangeinterpolationwith

6、algebraicmethodsinceGr5bnerbasessuggestingthat，canbeusedbecomespoesibiUtyInchapterfour，wegiveoutthealgorRhmthatGr6bnermethodandCoCoAprogrammingmethodcalculatingmultivariateLagrangeinterpolationbasesandseveralexamplesThef