Research On Multivariate Osculatory Interpolation

Content:Interpolation is a very classic problem of Mathematics and also a basic problem in computational Mathematics.It is well known that univariate interpolation has a very well developed theory and method.However,since 1980's,people come to turn the research of interpolation on multivariate interpolation,the reason is that multivariate interpolation has a widespread application in many fields,such as surfaces design,multivariate function arrange figures and finite element method.At the same time,since the algebraic geometry theory and method during the past few years have unceasingly developed and improved,we have forceful theory basis and new method to further research the problem of multivariate interpolation.In this paper,there are four sections.In the first section,we introduce the basic theory.In the second section,we give out the recent main results of multivariate Lagrange interpolation.In the third section,we mainly deals with the related problems of approaching the twice continuous-differential function on Simplex Integrations with the binary quadratic polynomial.In the four section,we give a kind of method of construction method,we still give an alogrithm for computing Lagrange interpolation polynomial on sphere.and wo give a piecewise interpolation polynomial on sphere and its error estimate.