Smooth fractal interpolation

By María A. Navascués, M. Sebastián. 2006

92 citations recorded by the source corpus.

Fractal methodology provides a general frame for the understanding of real-world phenomena. In particular, the classical methods of real-data interpolation can be generalized by means of fractal techniques. In this paper, we describe a procedure for the construction of smooth fractal functions, with the help of Hermite osculatory polynomials. As a consequence of the process, we generalize any smooth interpolant by means of a family of fractal functions. In particular, the elements of the class can be defined so that the smoothness of the original is preserved. Under some hypotheses, bounds of the interpolation error for function and derivatives are obtained. A set of interpolating mappings associated to a cubic spline is defined and the density of fractal cubic splines in is proven.

Subfields: Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/4e792f34eda309d379a01ae5881c93ddd50c4041

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Mathematical Physics

1. Arya Kumar Bedabrata Chand
2. María A. Navascués

Citations in the corpus

• Fundamental Sets of Fractal Functions (2008, methodology): “The power of that methodology allows us to generalize almost any other interpolation techniques [6, 17–19].”