In the contribution, we are concerned with the exact interpolation of the data at nodes given and also with the smoothness of the interpolating curve and its derivatives. This task is called the problem of smooth approximation of data. The interpolating curve or surface is defined as the solution of a variational problem with constraints. We discuss the proper choice of basis systems for this way of approximation and present the results of several 1D numerical examples that show the quality of smooth approximation.
@article{702910,
title = {Smooth approximation and its application to some 1D problems},
booktitle = {Applications of Mathematics 2012},
series = {GDML\_Books},
publisher = {Institute of Mathematics AS CR},
address = {Prague},
year = {2012},
pages = {243-252},
mrnumber = {MR3204416},
zbl = {1313.65017},
url = {http://dml.mathdoc.fr/item/702910}
}
Segeth, Karel. Smooth approximation and its application to some 1D problems, dans Applications of Mathematics 2012, GDML_Books, (2012), pp. 243-252. http://gdmltest.u-ga.fr/item/702910/