Energy minimizing associate fractal functions

Original Paper
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Abstract

The object of this paper is twofold. First, a basic question on fractal function from the perspective of numerical analysis, namely, how to evaluate a Fractal Interpolation Function (FIF) at a prescribed point is addressed by an appeal to a series expansion for FIF. Second is related to the notion of \(\alpha \)-fractal function, which we call associate fractal function, in the field of fractal approximation. We provide strategies for effective choices of scaling parameters in the associated fractal function. To this end, we minimize some functionals, such as square integral, which represents the total energy or power of a continuous-time signal and Holladay functional, which approximates the total bending energy.

Keywords

Fractal interpolation function Associate fractal function Convex optimization Energy minimizing integral Holladay functional 

Mathematics Subject Classification

97N50 58C05 28A80 46N10 26A18 

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Copyright information

© Springer-Verlag Italia S.r.l., part of Springer Nature 2018

Authors and Affiliations

  1. 1.Departmento de Matemática Aplicada, Escuela de Ingeniería y ArquitecturaUniversidad de ZaragozaZaragozaSpain
  2. 2.Department of MathematicsIndian Institute of Technology DelhiNew DelhiIndia

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