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Some computational aspects of smooth approximation

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Abstract

The paper is devoted to the problem of smooth approximation of data. We are concerned with the exact interpolation of the data at nodes and, at the same time, with the smoothness of the interpolating curve and its derivatives. The same procedure is applied to the fitting of data (smoothing of data), too. The approximating curve is defined as the solution of a variational problem with constraints (interpolation conditions at nodes, data fitting property of the curve) the existence of whose unique solution we prove. Except for the constraints, the formulation of the problem of data approximation is not unique in general as our requirements on the behavior of the approximating curve between the nodes can be very subjective. The smooth approximation of this kind can lead, e.g., to the cubic spline interpolation.We discuss the choice of basis systems for this way of approximation and present results of several 1D numerical examples that show some advantages and drawbacks of smooth approximation.

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Acknowledgments

This research has been supported by the Institute of Novel Technologies and Applied Informatics, Faculty of Mechatronics, Informatics and Interdisciplinary Studies, Technical University of Liberec.

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  1. Technical University of Liberec, Studentská 2, Liberec, 461 17, Czech Republic

    Karel Segeth

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  1. Karel Segeth
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Correspondence to Karel Segeth.

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Segeth, K. Some computational aspects of smooth approximation. Computing 95 (Suppl 1), 695–708 (2013). https://doi.org/10.1007/s00607-012-0252-6

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  • DOI: https://doi.org/10.1007/s00607-012-0252-6

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