Boundary interpolation on triangles via neural network operators

Aaqib Ayoub Bhat and Asif Khan

Mathematics and Computers in Simulation (MATCOM), 2026, vol. 241, issue PA, 190-201

Abstract: The primary objective of this study is to develop novel interpolation operators that interpolate the boundary values of a function defined on a triangle. This is accomplished by constructing new Generalized Boolean sum neural network operator Bn1,n2,ξℱ using a class of activation functions. Its interpolation properties are established and the estimates for the error of approximation corresponding to operator Bn1,n2,ξℱ is computed in terms of mixed modulus of continuity. Numerical examples are illustrated to show the efficacy of these newly constructed operators. Further, with the help of MATLAB (2024a), comparative and graphical analysis is given to show the validity and efficiency of the results obtained for these operators.

Keywords: Neural network operators; Sigmoidal function; Interpolation; Generalized Boolean sum operators; Mixed modulus of continuity; Quantitative estimates (search for similar items in EconPapers)
Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:241:y:2026:i:pa:p:190-201

DOI: 10.1016/j.matcom.2025.08.026

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