Numerical integration of affine fractal functions

• Autores: María Antonia Navascués Sanagustín , María Victoria Sebastián
• Localización: Journal of computational and applied mathematics, ISSN 0377-0427, Vol. 252, Nº 1, 2013, págs. 169-176
• Idioma: inglés
• DOI: 10.1016/j.cam.2012.09.029
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• Resumen

  • This paper studies a method for the numerical integration and representation of functions defined through their samples, when the original ��signal�� is not explicitly known, but it shows experimentally some kind of self-similarity. In particular, we propose a methodology based on fractal interpolation functions for the computation of the integral that generalize the compound trapezoidal rule. The convergence of the procedure is proved with the only hypothesis of continuity. The rate of convergence is specified in the case of original Hölder-continuous functions, but not necessarily smooth.