Smooth approximation spaces based on a periodic system

0443851 - MÚ 2016 RIV CZ eng C - Conference Paper (international conference)
Segeth, Karel
Smooth approximation spaces based on a periodic system.
Programs and algorithms of numerical mathematics 17. Proceedings of seminar. Praha: Matematický ústav AV ČR, v.v.i, 2015 - (Chleboun, J.; Přikryl, P.; Segeth, K.; Šístek, J.; Vejchodský, T.), s. 194-199. ISBN 978-80-85823-64-6.
[Programs and Algorithms of Numerical Mathematics /17./. Dolní Maxov (CZ), 08.06.2014-13.06.2014]
R&D Projects: GA ČR GA14-02067S
Institutional support: RVO:67985840
Keywords : smooth interpolation * data interpolation * cubic spline interpolation
Subject RIV: BA - General Mathematics
http://hdl.handle.net/10338.dmlcz/702684

A way of data approximation called smooth was introduced by Talmi and Gilat in 1977. Such an approach employs a (possibly infinite) linear combination of smooth basis functions with coefficients obtained as the unique solution of a minimization problem. While the minimization guarantees the smoothness of the approximant and its derivatives, the constraints represent the interpolating or smoothing conditions at nodes. In the contribution, a special attention is paid to the periodic basis system $exp(-ii kx)$. A 1D numerical example is presented.
Permanent Link: http://hdl.handle.net/11104/0246500