Numerical Analysis of the Method of Differentiation by Means of Real h-Sums

Abstract

We propose a numerical method of test algebraic polynomials for constructing the operators \( \sum_{k=1}^n{\uplambda}_kh\left({\uplambda}_kz\right) \) with odd n, real λ_k, and an even analytic function h(z) in a neighborhood of the origin that approximate the differential operator (zh(z))′ with local error O(zⁿ⁺²) (z → 0), n ≤ 51.