https://doi.org/10.1140/epjs/s11734-023-00864-y
Regular Article
Numerical integration of bivariate fractal interpolation functions on rectangular domains
Department of Mathematics, Amrita School of Physical Sciences, Amrita Vishwa Vidyapeetham, Coimbatore, India
b
p_paramanathan@cb.amrita.edu
Received:
7
December
2022
Accepted:
3
May
2023
Published online:
5
June
2023
This paper primarily focuses on the derivation of fractal numerical integration for the data sets corresponding to two variable signals defined over a rectangular region. Evaluating numerical integration results through the fractal method helps achieve accurate results with minimum computation effort. The formulation of the fractal numerical integration is achieved by considering the recursive relation satisfied by the bivariate fractal interpolation functions for the given data set. The points in the data set have been used to evaluate the coefficients of the iterated function systems. The derivation of these coefficients considering the index of the subrectangles, and the integration formula has been proposed using these coefficients. The bivariate fractal interpolation functions constructed using these coefficients are then correlated with the bilinear interpolation functions. Also, this paper derives a formula for the freely chosen vertical scaling factor that has been used in reducing the approximation error. The obtained formula of the vertical scaling factor is then used in establishing the convergence of the proposed method of integration to the traditional double integration technique through a collection of lemmas and theorems. Finally, the paper concludes with an illustration of the proposed method of integration and the analysis of the numerical integral results obtained for the data sets corresponding to four benchmark functions.
Framework of Fractals in Data Analysis: Theory and Interpretation. Guest editors: Santo Banerjee, A. Gowrisankar.
Copyright comment Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
© The Author(s), under exclusive licence to EDP Sciences, Springer-Verlag GmbH Germany, part of Springer Nature 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
