張量積空間P-,m1,m2,…,ms-的多元Lagrange插值適定結(jié)點(diǎn)組.pdf

1、東北師范大學(xué)碩士學(xué)位論文張量積空間P的多元Lagrange插值適定結(jié)點(diǎn)組姓名：李冰玉申請(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：盛中平2003.5.1AbstractInthispaper，weconstructaclassofproperlyposedsetofnodes(orPPSN，forshort)formultivariateLagrangeinterpolationabouttheinter—polationplaceoffk

2、l㈣，m(S2)，afterwestudythegeometricstruc—tureofPPSNalonganalgebraichyperplanexj—a=0，1SJ≤sInthisway，wecangeneralizethetechniqueaboutR，nin【2jDefinitionLetxj—a=0，1SJ≤sbeanalgebraichyperplaneinCLand吼)恕lbe女=(ml1)(mJ一11)(mjl1)‘‘

3、(ms1)distinctpointsono。一a；0Ifrelationsp(x)∈pmⅢ。m，P(qi)一0，i=1，，kimplyp(x1蘭0onxj一8=0wecall黿整laPPSNalongthealgebraichyperplane％一a一0Theorem1Let靠冬lbe氌PPSNinC8about冀m，m2，，m；，whicharenotOnanalgebraichyperplanezJ—a=0，1≤J≤s，and舔冬

4、lbeaPPSNalongthealgebraichyperplane％一a=0about瑋“，m，州11m川，弗，，thenthesetof協(xié)i：lUqii：=lmustbeaPPSNinC5aboutR，mj“mjl，％mTheorem2LetR=《≥lbeonanalgebraichyperplanexj一8=0(I≤J≤8)inC8，thenRisaPPSNalongxj—a20about乓，m，“碑l粥l(xiāng)，，‰ifandonl

5、yifRisaPPSN。fjk|’“，mi“。，秘l，，‰Theorem3LetQl—m，l一1bePPSNsaboutPm2m，，maQ=銣)：l，qij=(毋’，，磚1)，J—l，2，，％。Freelyselectml1distinctalgebraichyperplanesxi—ai=0，i=1，2，，ml‘十1，thenmustbeaPPSNabout島Hm：minC8Keywords：multivariateLagrangei