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 $exp(-kx)$. A 1D numerical example is presented.

EUDML-ID : urn:eudml:doc:269901
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@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/