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Article

Segeth, Karel
Smooth approximation and its application to some 1D problems. (English). In: Brandts, J., Chleboun, J., Korotov, S., Segeth, K., Šístek, J. and Vejchodský, T. (eds.): Applications of Mathematics 2012, In honor of the 60th birthday of Michal Křížek. Proceedings. Prague, May 2-5, 2012. Institute of Mathematics AS CR, Prague, 2012. pp. 243-252
MSC: 41A05, 41A29, 65D05, 65T40 | MR 3204416 | Zbl 1313.65017
Keywords:
smooth approximation; variational problem with constraints; numerical example; interpolation of scattered data; rational function interpolation
Summary:
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.
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