Rocky Mountain Journal of Mathematics

Interpolation mixing hyperbolic functions and polynomials

J.M. Carnicer, E. Mainar, and J.M. Peña

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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.

Article information

Source
Rocky Mountain J. Math., Volume 48, Number 2 (2018), 443-461.

Dates
First available in Project Euclid: 4 June 2018

Permanent link to this document
https://projecteuclid.org/euclid.rmjm/1528077625

Digital Object Identifier
doi:10.1216/RMJ-2018-48-2-443

Mathematical Reviews number (MathSciNet)
MR3810207

Zentralblatt MATH identifier
06883475

Subjects
Primary: 41A05: Interpolation [See also 42A15 and 65D05] 41A30: Approximation by other special function classes 65D05: Interpolation

Keywords
Hyperbolic functions Hermite interpolation Newton and Aitken Neville formulae total positivity shape preserving representations

Citation

Carnicer, J.M.; Mainar, E.; Peña, J.M. Interpolation mixing hyperbolic functions and polynomials. Rocky Mountain J. Math. 48 (2018), no. 2, 443--461. doi:10.1216/RMJ-2018-48-2-443. https://projecteuclid.org/euclid.rmjm/1528077625


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