Interpolation mixing hyperbolic functions and polynomials

Abstract

Exponential polynomials as solutions of differential equations with constant coefficients are widely used for approximation purposes. Recently, mixed spaces containing algebraic, trigonometric and exponential functions have been extensively considered for design purposes. The analysis of these spaces leads to constructions that can be reduced to Hermite interpolation problems. In this paper, we focus on spaces generated by algebraic polynomials, hyperbolic sine and hyperbolic cosine. We present classical interpolation formulae, such as Newton and Aitken-Neville formulae and a suggestion of implementation. We explore another technique, expressing the Hermite interpolant in terms of polynomial interpolants and derive practical error bounds for the hyperbolic interpolant.