On A Kind Of Modifying Lagrange Interpolation Formula

As is well known, polynomial operator (including algebra polynomials and triangle polynomials) is always used to approximate functions and becomes a quite effective tool in numerical approximation theory. However, Lagrange interpolation polynomial is more important than others, and it is well used in nature science, engineering technology area, and so on. In particular, many numerical methods and other similar interpolation polynomials are derived from the Lagrange interpolation polynomial. From the known Faber's theorem and the known Bernstein's theorem, we know that Lagrange interpolation polynomial does not converge uniformly to arbitrary continuous functions, and thus how to improve its convergence properties becomes an important object.Many scholars have been attracted in this area and many significant improvements have been made since then, such as, Bernstein who is a famous mathematician of Soviet...