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2006•Journal of Liaoning Normal UniversityRequires access

Some Researches of Bivariate Hermite Interpolation

Mian Li

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Abstract

In this paper,some problems on bivariate Hermite interpolation by polynomial are studied.The concepts of strong H-basis and Hermite interpolation along a plane algebraic curve are proposed.As a result,the general methods for constructing the unisolvent set for bivariate Hermite interpolation in R~2 and along a plane algebraic curve are deduced,respectively.This generalizes the main results acquired by H.A.Hakopian,Borislar Bojanov and Xu Yuan in 2002 and 2003,respectively.

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What this paper is about

In this paper,some problems on bivariate Hermite interpolation by polynomial are studied.The concepts of strong H-basis and Hermite interpolation along a plane algebraic curve are proposed.As a result,the general methods for constructing the unisolvent set for bivariate Hermite interpolation in R~2 and along a plane algebraic curve are deduced,respectively.This generalizes the main results acquired by H.A.Hakopian,Borislar Bojanov and Xu Yuan in 2002 and 2003,respectively.

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Available abstract

In this paper,some problems on bivariate Hermite interpolation by polynomial are studied.The concepts of strong H-basis and Hermite interpolation along a plane algebraic curve are proposed.As a result,the general methods for constructing the unisolvent set for bivariate Hermite interpolation in R~2 and along a plane algebraic curve are deduced,respectively.This generalizes the main results acquired by H.A.Hakopian,Borislar Bojanov and Xu Yuan in 2002 and 2003,respectively.

Key concepts: Hermite interpolation, Birkhoff interpolation, Mathematics, Interpolation (computer graphics), Bivariate analysis, Cubic Hermite spline, Hermite polynomials, Algebraic number

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