We study the polynomial approximation of symmetric multivariate functions and multi-set functions. Specifically, we consider f (</mml...

Due to the Lagrange interpolation polynomials do not converge uniformly to arbitrary continuous functions, in this paper, a new interpolation polynomial is constructed by using the weighted average method to the interpolated functions. It is proved that the interpolation polynomial not only converges uniformly to arbitrary continuous functions, but also has the best approximation order and the ...

The polynomial of degree n which is the best approximation of the sinc function on the interval 0, π/2 with the square norm is considered. By using Lagrange's method of multipliers, we construct the polynomial explicitly. This method is also generalized to the continuous function on the closed interval a, b. Numerical examples are given to show the effectiveness.