Reproduction Capabilities of Penalized Hyperbolic-polynomial Splines

DOI10.1016/J.AML.2022.108133zbMATH Open1524.41019arXiv2202.06678WikidataQ115597720 ScholiaQ115597720MaRDI QIDQ6391054

Constanza Conti, Rosanna Campagna

Publication date: 14 February 2022

Abstract: This paper investigates two important analytical properties of hyperbolic-polynomial penalized splines, HP-splines for short. HP-splines, obtained by combining a special type of difference penalty with hyperbolic-polynomial B-splines (HB-splines), were recently introduced by the authors as a generalization of P-splines. HB-splines are bell-shaped basis functions consisting of segments made of real exponentials $e^{alphax},,e^{-alphax}$ and linear functions multiplied by these exponentials, $x{e}^{+alphax}$ and $x{e}^{-alphax}$. Here, we show that these type of penalized splines reproduce function in the space $e^{-alphax},x{e}^{-alphax}$, that is they fit exponential data exactly. Moreover, we show that they conserve the first and second 'exponential' moments.

Mathematics Subject Classification ID

Numerical computation using splines (65D07) Spline approximation (41A15)

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