Study On The Tangent Interpolation Problem Of Sphere

In this paper,the problem of multi-element contact interpolation defined on sphere is studied and discussed.In the first part,the problem of multi-element contact interpolation is introduced,including the problem of multi-element contact interpolation and its classification.This part is divided into three sections,In the first section,the basic problem of multivariate polynomial interpolation is proposed;in the second section,the classical scheme of multivariate contact interpolation is introduced;in the third section,the basic concept of generalized contact interpolation is introducedIn the second part,some preliminary knowledge of binary contact interpolation is introduced.Firstly,some related theories of binary contact interpolation are described.Secondly,the Gasca maeztu method of binary contact interpolation is introduced,that is,the extension of linear superposition interpolation method.Finally,the superposition interpolation method of binary contact interpolation is introduced.The advantage of this method is that it has some irregular interpolation conditions,It can guarantee the existence and uniqueness of interpolation scheme,and can easily construct a specific contact interpolation schemeThe third part is the core content of this paper.On the basis of the previous research,this paper further studies the multi-element contact interpolation of the sphere.By using the superposition interpolation method,we construct the three-element quadratic and three-element cubic contact interpolation well-defined functional groups,expand the three-element contact interpolation formula,and give the corresponding theorem proof,at last,the experimental results of the trigonometric quadratic and trigonometric contact interpolation are used,and the errors of the two examples are compared and analyzed with MATLAB...