Integral refinable operators exact on polynomials
\textit{L. Gori, F. Pitolli, E. Santi} [Numer. Algorithms 28, No. 1-4, 199--213 (2001; Zbl 0993.65157)] studied refinable integral operators of Bernstein-Durrmeyer type. Those operators reproduce only the constant functions. Here the authors construct generalized refinable integral operators that reproduced polynomials of degree \(2m\) with \(0\leq 2m\leq n-2,\) having assumed that the basis functions, utilized for constructing the operators, have order of polynomial reproducibility \(n-2.\) The \(L^p\) norm of these operators is estimated, error bounds for approximation of functions and their derivatives in suitable classes are given. Numerical results and comparisons with other quasi-interpolatory operators having the same order of polynomial reproducibility are presented.
scientific article; zbMATH DE number 5355704
scientific article