The Method Of Constructing Bivariate Hermite Interpolation Formula

Interpolation is a very classic problem in computational Mathematics and also a important content which has widely attention and research. It is well known that univariate interpolation has a very well developed theory, method and practical applicationg by many researchers hard work. However, since many years, people come to turn to the research of interpolation on multivariate interpolation. Many researchers gived out a lot of theories and methods which have research value and applicational value about multivariate. The reason of the attention about multivariate interpolation is that multivariate interpolation has a widespread application in many fields.(such as, surfaces design, finite element method and multivariate function arrange figures, and so on.) This paper has divided into three chapters. The first chapter is introduction and it is divided into two sections. In this chapter, we have introduced that the theories and affection about multivariate interpolation by many researchers and the methods of making the fomulas of multivariate interpolation. The second chapter is preliminaries. In this chapter, we have introduced many theories, fomulas and examples which we need. The third chapter is constructing bivariate Hermite interpolation polynomial, this chapter is the most important content. In the third chapter, we have constructed the four item of bivariate Hermite interpolation polynomial which based on the superposition interpolation, and an example is given to verify the effectiveness of Hermite interpolation polynomial. And we must notice that, in this chapter we also use MATLAB to run the image of the multivariate interpolation polynomials, and we have verificated a very important conclution.