A particular smooth interpolation that generates splines

0475635 - MÚ 2018 RIV CZ eng C - Conference Paper (international conference)
Segeth, Karel
A particular smooth interpolation that generates splines.
Programs and algorithms of numerical mathematics 18. Prague: Institute of Mathematics CAS, 2017 - (Chleboun, J.; Kůs, P.; Přikryl, P.; Segeth, K.; Šístek, J.; Vejchodský, T.), s. 112-119. ISBN 978-80-85823-67-7.
[Programs and Algorithms of Numerical Mathematics /18./. Janov nad Nisou (CZ), 19.06.2016-24.06.2016]
R&D Projects: GA ČR GA14-02067S
Institutional support: RVO:67985840
Keywords : data interpolation * smooth interpolation * spline interpolation
OECD category: Applied mathematics
http://hdl.handle.net/10338.dmlcz/703005

There are two grounds the spline theory stems from -- the algebraic one (where splines are understood as piecewise smooth functions satisfying some continuity conditions) and the variational one (where splines are obtained via minimization of some quadratic functionals with constraints). We use the general variational approach called $it smooth interpolation$ introduced by Talmi and Gilat and show that it covers not only the cubic spline and its 2D and 3D analogues but also the well known tension spline (called also spline with tension). We present the results of a 1D numerical example that characterize some properties of the tension spline.
Permanent Link: http://hdl.handle.net/11104/0272303