A note on tension spline. (English) Zbl 1363.65021

Segeth, Karel

Brandts, J. (ed.) et al., Proceedings of the international conference ‘Applications of mathematics’, Prague, Czech Republic, November 18–21, 2015. In honor of the birthday anniversaries of Ivo Babuška (90), Milan Práger (85), and Emil Vitásek (85). Prague: Czech Academy of Sciences, Institute of Mathematics (ISBN 978-80-85823-65-3). 217-224 (2015).

A general variational approach of Talmi and Gilat for obtaining smooth interpolation curves, called smooth interpolation, is described and explained. Author focuses on two important special cases, namely cubic spline and spline with tension, and shows how they can be computed using this general approach, by means of Fourier transform. Behavior of these two types of splines is compared and graphically illustrated on a 1D example.
For the entire collection see [Zbl 1329.00187].

Reviewer: Marta Čertíková (Praha)

MSC:

65D07	Numerical computation using splines
65D05	Numerical interpolation
41A05	Interpolation in approximation theory
65T50	Numerical methods for discrete and fast Fourier transforms

Keywords:

smooth interpolation; tension spline; Fourier transform; interpolation curves; cubic spline