Parameter Identification for a Class of Bivariate Fractal Interpolation Functions and Constrained Approximation. (3rd July 2020)

• Record Type: Journal Article
• Authors: Verma, S.; Viswanathan, P.
• Is Part Of: Numerical functional analysis and optimization. Volume 41:Number 9(2020)
• Page Start: 1109
• Page End: 1148
• Publication Date: 2020-07-03
• Subjects: Box dimension -- constrained approximation -- fractal interpolation function -- hausdorff dimension -- parameter identification; 28A80 -- 41A29 -- 41A30; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2020.1738458
• Languages: English
• ISSNs: 0163-0563

Abstract

Abstract: The current article intends to study some elementary constrained approximation aspects of the bivariate fractal functions. To this end, firstly the construction of bivariate fractal interpolation functions available in the literature is revisited with a focus to obtain a parameterized family of fractal functions corresponding to a prescribed bivariate continuous function on a rectangular region in R 2 . The parameters are chosen appropriately so that the corresponding fractal version preserves some properties inherent in the original function. We apply these results to invite the notion of bivariate fractal functions to the field of constrained approximation. Furthermore, we attempt to investigate the box dimension and Hausdorff dimension of the graph of the constructed bivariate fractal function.