关于Lagrange插值多项式的一致收敛性

Uniform Convergence of Lagrange Interpolation Polynomials

为了改进Lagrange插值多项式的一致收敛性,基于第三型Bernstein插值过程构造了两类插值多项式,给出了两类插值多项式的最佳逼近阶和最高收敛阶.

To improve the uniform convergence of the Lagrange interpolation polynomial, two interpolation polynomials are constructed based on the Bernstein interpolating process of the third type. The best approximation order and the highest convergence order of the interpolation polynomials are presented.