New Methods To Construct Bivariate Osculatory Interpolation Scheme

As is known to all: the study of Multivariate Os culatory interpolation is further extended on the developm ent of the Osculatory inte rpolation. The m ost general m ethod before structuring a multivariate Osculatory format is determinant method. However, the method will be difficult to use if there are many interpolation conditions, especially when the co nditions are selected inappropriately probably it m ay cannot calculat e the interpolation for mat(interpolation function). In the current scores of years, wi th the development of science and technology in the world, som e research and pr oduction departments are often need to use multivariate osculatory interpolation to com plete some scientific tasks. Becau se of the diversity of interpolation nodes distribution and the com plexity of interpolation interval, the previous literature researched more on m ultivariate interpolation problems in rectangular network. Whereas the author uses the m ethod of iterated interpolation proposed by Professor Liang Xuezhang to construct bivariate osculatory interpolation scheme in this application, this method may allow some irregular interpolation conditions. It first fixes interpo lation node to construct polynomial which can satisfy the inte rpolation conditions, and then calculates the coefficients of the polynom ials, and through th e example of absolute error interpolation polynomial and the prim ary function value to veri fy the effectiveness of this m ethod. This method can guarantee the existence and uniqueness of the interpolation polynomial, and it is convenient to obtain the specific interpolation scheme. Based on the existing results, this thesis constructs the bivariate osculatory interpolation scheme on th e circular an d curve domain to illus trate how to app ly the superposition interpolation to construct bivar iate osculatory interpolation scheme.This thesis has two parts:The first chapter introduces the primary knowledge of multivariate interpolation.It briefly introduces the basic co ncepts and definitions of multivariate interpolation and Multivariate Rational Interpolation and th e related theorem, finally it introduces the background knowledge closely relating to osculatory interpolation.The second chapter first introd uces a ne w way to co nstruct multivariate osculatory interpolation, including iterated interpolation method and related theories and m ethods, and finally, the author uses this method to construct a class of parabolic curve domain and the unit circle domain interpolation schem e, what is m ore, some numerical examples to verify the effectiveness of the method are also given.