Approximation by Baskakov quasi-interpolants

TL;DR

This paper introduces Baskakov quasi-interpolants, derived from Baskakov operators expressed as differential operators, providing recurrence relations, asymptotic convergence analysis, and numerical examples for function approximation on the positive real line.

Contribution

It presents a novel construction of Baskakov quasi-interpolants with recurrence formulas and asymptotic convergence results, enhancing approximation techniques for functions on the positive real half-line.

Findings

Recurrence relations for Baskakov quasi-interpolants derived.

Asymptotic convergence orders established.

Numerical examples demonstrate effective approximation.

Abstract

Baskakov operators and their inverses can be expressed as linear differential operators on polynomials. Recurrence relations are given for the computation of these coefficients. They allow the construction of the associated Baskakov quasi-interpolants (abbr. QIs). Then asymptotic results are provided for the determination of the convergence orders of these new quasi-interpolants. Finally some results on the computation of these QIs and the numerical approximation of functions defined on the positive real half-line are illustrated by some numerical examples.