Convergence order of interpolation process by Bernstein polynomials
The convergence order of the interpolation process by S. N. Bernstein polynomials \(F_ n(f,x)\) with zeros of a Chebyshev polynomial of first kind of degree n is considered. We prove the following result: the convergence order is \[ \frac{1}{n}\omega (f',\frac{\sqrt{k-x^ 2}}{n}+\frac{1}{n^ 2})+\frac{\| f'\|}{n^ 2} \] when using the interpolation process \(F_ n(f,x)\) to approximate \(f(x)\in C^ 1[-1,1]\) on [-1,1].
scientific article; zbMATH DE number 4124301