Bivariate Hermite interpolation

André Hirschowitz

Description

Bivariate Hermite Interpolation Hirschowitz The problem The conjectures The results so far Nagata's conjecture Methods Conclusion Bivariate Hermite Interpolation Andre Hirschowitz 1 1CNRS, UNS Nice 10/6/2009

• easy remarks


• passing through


• interpolation


• bivariate hermite


• map ev


• necessary condition

Sujets

• Passing Through
• Interpolation
• Necessary and sufficient condition

Informations

• Publié par: pefav
• Nombre de lectures: 12
• Langue: English

Extrait

eciN 10/6/2009 1 CNRS,UNS Andre´Hirschowitz 1 BivariateHermiteInterpolation noisulcnoC sdohteM erutcejnoc s’atagaN rafosstluserehT serutcejnocehT melborpehT ztiwohcsriH noitalopretnI etimreHetairaviB

noisulcnoC sdohteM erutcejnoc s’atagaN rafosstluserehT serutcejnocehT melborpehT ztiwohcsriH noitalopretnI etimreHetairaviB 6 Conclusion 5 Methods Theresultssofar 3 4 Nagata’sconjecture Theproblem 1 Theconjectures 2

noisulcnoC sdohteM erutcejnoc s’atagaN rafosstluserehT serutcejnocehT melborpehT ztiwohcsriH noitalopretnI etimreHetairaviB Chooseanumberofvariablesn(defaultvaluen:=2) Chooseadegreed,anumberofpointsr Chooseamultiplicitysequencem:=(m 1 , ∙∙∙ ,m r ) Chooserpointsp:=(p 1 ,...,p r )in R n (verygeneral) Searchapolynomialofdegreeatmostdwith prescribedvaluesandderivativesuptoorderm i − 1at p i foreachi. Thisamountstosearchasectionofthegeneralized evaluationev: R [x 1 ,x 2 ] d → R p,m HermiteInterpolation

noisulcnoC sdohteM Weareonlyinterestedintheexistenceofasection e henceinthesurjectivityofourmap ev: R [x 1 ,x 2 ] d → R p,m . r Neces ( s d a + ry 1)( c d o + n 2 d ) itiono m n i ( d m i i m + e 1) nsions: χ:= 2 − Σ i 2 ≥ 0. Isitsufficient? u Inotherwords,isthedimensionofKerevasexpected? t Easyremarks cejnoc s’atagaN rafosstluserehT serutcejnocehT melborpehT ztiwohcsriH noitalopretnI etimreHetairaviB