Simultaneous Polynomial Approximation in the Weighted Chebyshev Norm

Simultaneous approximation means that a given sufficiently smooth function g:-1, 1] and its derivatives up to order q are approximated by a single polynomial p and its derivatives. This paper deals with new error estimates (in a weighted norm with explicit constants) and corresponding algorithms in the most interesting cases q = 1 and q = 2. The described method is based on the close relationship between algebraic and trigonometric polynomial approximation.