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 . A 1D numerical example is presented.
@article{702684,
title = {Smooth approximation spaces based on a periodic system},
booktitle = {Programs and Algorithms of Numerical Mathematics},
series = {GDML\_Books},
publisher = {Institute of Mathematics AS CR},
address = {Prague},
year = {2015},
pages = {194-199},
url = {http://dml.mathdoc.fr/item/702684}
}
Segeth, Karel. Smooth approximation spaces based on a periodic system, dans Programs and Algorithms of Numerical Mathematics, GDML_Books, (2015), pp. 194-199. http://gdmltest.u-ga.fr/item/702684/