Fractal splines

• Autores: María Victoria Sebastián, María Antonia Navascués Sanagustín
• Localización: Ninth international conference Zaragoza-Pau on applied mathematics and statistics: Jaca (Spain). September 19-21, 2005 / coord. por Monique Madaune-Tort, 2006, ISBN 84-7733-871-X, págs. 161-168
• Idioma: inglés
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• Resumen

  • Fractal methodology provides a general setting for the understanding of realworld phenomena. In particular, the classical methods of real-data interpolation can be generalized by means of fractal techniques. In this paper we use this kind of procedures to define a family of interpolating mappings associated to a cubic spline. This fact adds a ¿degree of freedom¿ to the function, allowing to preserve or modify its properties. In particular, the elements of the class can be defined so that the smoothness of the original be preserved. Under some hypotheses, and using Hermite polynomial techniques, bounds of the interpolation error for function and derivatives are obtained