Research On Multivariate Hermite Interpolation

Multivariate interpolation problem is a very important issue in computationalmathematics, discussion and research of some of the problems of multivariatepolynomial Hermite interpolation.The concepts of strong H-basis and Hermiteinterpolation along a plane algebraic curve are proposed.In this paper, starting from themultivariate interpolation a branch of binary Hermite interpolation multivariate Hermiteinterpolation discussions and research to promote binary graded Hermite interpolationproblem.In this thesis, we divided three parts. The first part we introduce the multivariateHermite interpolation problem formulation and some basic concepts and results ofprevious studies are summarized. Bézout theorem and Cayley-Bacharach Theoremconclusions and methods using algebraic geometry, given R2Hermite interpolation ofbinary appropriate geometry and geometric characteristics of the given functionalgroup.The second part we introduce the multivariate Hermite interpolation along thesurfaces algebraic curves and space along two aspects of some of the theories andresults.The third part we give the structure of bivariate polynomial space gradedHermite interpolation the main results.