Bivariate Lagrange Interpolation And H-Base

Interpolation problem has always been classic and basic research problems in computational mathematics discipline, in recent years, along with the multivariate interpolation is widely used in people in real life production, such as the object surface shape design, search for and development of mineral resources, geological simulation, neural network system and so on many aspects in the field of practical application, makes the interpolation problem is one of the topic more and more get the attention of people, one yuan polynomial interpolation problem research has tended to be perfect, since the1980s people will be focused on the research into the multivariate interpolation, and the focus of this paper is mainly for the binary interpolation problem. In1965, professor Liang XueZhang in literature [1] for the first time puts forward the concept of bivariate interpolation well-posed node set, are constructing bivariate polynomial interpolation well-posed node group a practical recursive method, for further research, in1998, professor Liang XueZhang and Dr Lv Chunmei along the plane algebraic curve interpolation is proposed for the first time the basic concept, and puts forward along the plane algebraic curve interpolation of a recursive method, moreover, Liang and Lu also studied the well-posed along the structural plane algebraic curve interpolation nodes set to add the straight-line method and adding the cone curve method.In this paper, the research mainly is continue and deepen the study, we get the main results are as follows:(1)Further discussion and study of bivariate interpolation problem, by introducing the basic concepts in algebraic geometry and use the famous theorem and conclusion, the well-posed plane algebraic curve interpolation nodes set of general construction method and more profound theoretical results, and gives some practical reasoning, so as to further understand the well-posed node set of bivariate interpolation basic characteristics and geometry.(2) Further generalize the Liang and Lu well-posed of along the structural plane algebraic curve interpolation nodes group to add plane method, and USES the method of interpolation in algebraic geometry is the famous theorem for the new certificate.This article altogether is divided into four parts, first is the full text of the introduction section, the first chapter mainly introduces multivariate interpolation used in the field of mathematical terms and basic theory, the second chapter mainly by introducing some practical conclusions and theorem, the interpolation method was mainly used for famous theorem for the new certificate.