Mathematical Modeling
Vol. 9 (2025), Issue 1, pg(s) 3-10

THEORETICAL FOUNDATIONS AND SPECIFICITY OF MATHEMATICAL MODELLING

Improved RBF Method for High-Accuracy Reconstruction of Complex Two- Dimensional Fields

  • 1 Polytechnic University of Tirana, Tirane, Faculty of Mathematical & Physical Engineering

Abstract

Radial Basis Function (RBF) interpolation is widely used for reconstructing scattered multidimensional data, but its accuracy and stability often depend heavily on the point distribution, kernel choice, and matrix conditioning. This work proposes an improved RBF framework that combines a whitening transformation, adaptive sampling, and cross-validated parameter tuning to obtain more reliable reconstructions of complex two-dimensional fields. Whitening reduces geometric distortions and improves conditioning, while the adaptive sampling strategy focuses points in regions with strong gradients. Tests on a deliberately challenging synthetic function show that the whitening-enhanced RBF model achieves higher stability and lower error (in L1, L2, and L∞ norms) compared to the standard RBF formulation. The method is implemented in Python using open-source libraries and performs efficiently even on modest hardware.

Keywords

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