Improving Coefficients Of Error Bounds For Lagrange Interpolation Polynomials

In computational mathematics and engineering, interpolation is an old and major research problem. However, Lagrange interpolation is more important than others. Since the nineteenth century, its research has been in progress. It is well known that the theory and method of univariate interpolation has a very well devel-oped. Multivariate interpolation becomes an important research since the eighties.The paper describes the concepts and theories related to Lagrange interpola-tion. Bivariate interpolation problem has been done a simple study and elaborated. In the fully absorb and digest foreign scholars on the error of Lagrange interpolation, several conclusions are drew. We estimate the upper bounds of the error terms for approximation using Lagrange interpolation polynomials with equally spaced nodes. This paper has four chapters:In the first chapter, it is introduced about the development of Lagrange inter-polation, our main study and its theoretical meaning and value.In the second chapter, it is described about the basic concept of univariate in-terpolation, Lagrange interpolation polynomial and its advantage and disadvantage. Then an example is cited to illustrate its practical application, which leads to the error of Lagrange interpolation polynomial.In the third chapter, it is summarized about the results of error of Lagrange interpolation polynomial, including the remaining items and two theories. Then they are proved. An example is used to show the error bound closer to the actual error. Finally, the coefficients of error bounds is improved, and proved. These conclusions and their proof are my main contributions in this paper.In the fourth chapter, some conclusions are simply described about the basic problem and the construction of properly posed set of nodes on bivariate interpola-tion, while others are described about the network of triangular Lagrange interpo-lation polynomial and bivariate Lagrange interpolation polynomial. Then, the error is estimated by Kincaid and the remaining items. Then it is simply improved.