Uniform reconstruction of continuous functions with the RAFU method

Eduardo Corbacho Cortés

Spain

IES Saenz de Buruaga (Badajoz)

Department of Mathematics

Submitted: 2017-02-12

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Accepted: 2017-04-10

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Published: 2017-10-02

DOI: https://doi.org/10.4995/agt.2017.7263
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Keywords:

RAFU method, RAFU approximation, uniform approximation

Supporting agencies:

This research was not funded

Abstract:

The RAFU (radical functions) method can be used to obtain the uniform reconstruction of a continuous function from its values at some of the points of partitions of a closed interval. In this work we will prove that we can reconstruct a continuous function from average samples of these points, from linear combinations of them and from local average samples given by convolution. Uniform error bounds will be established. If these data are unknown but approximate values of them are known, uniform reconstruction will be also possible. Error estimates in these cases will be given. The case of a non-uniform net will be treated. Examples and algorithms will be also shown.
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