https://doi.org/10.1140/epjs/s11734-025-01869-5
Regular Article
Bivariate Bernstein fractal interpolation and numerical integration on triangular domains
Department of Mathematics, Amrita School of Physical Sciences, Amrita Vishwa Vidyapeetham, Coimbatore, India
a
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Received:
7
March
2025
Accepted:
17
August
2025
Published online:
22
August
2025
The fundamental aim of this paper is to provide the approximation and numerical integration of a discrete set of data points with Bernstein fractal approach. In this paper, a numerical integration formula for the data set corresponding to univariate functions is proposed using Bernstein polynomials in the iterated function system. The convergence of the proposed formula of integration is investigated with the data sets of certain Weierstrass functions. The paper then extends the Bernstein fractal approximation and numerical integration technique to two-dimensional interpolating regions. Bernstein polynomials defined over triangular domain have been used for the purpose. Following the above-mentioned construction and approximation of bivariate Bernstein fractal interpolation functions, the paper introduces the numerical double integration formula using the constructed functions. The convergence of the double integration formula toward the actual integral value of the data sets is displayed with the help of some simulation examples including the benchmark functions. Both the newly introduced iterated function systems are verified for their hyperbolicity and the resultant fractal interpolation functions are shown to be continuous.
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© The Author(s), under exclusive licence to EDP Sciences, Springer-Verlag GmbH Germany, part of Springer Nature 2025
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.
