NUMERICAL COMPARISON OF THREE LOCAL MULTIVARIATE GAUSSIAN-BASED INTERPOLATION SCHEMES

This study introduces the Local Explicit Radial Basis Function scheme (LE-RBF), alongside an investigation of its effectiveness compared with two other Gaussian RBF-based methods: the Modified Radial Basis Function Shepard's method (MRBFS) and the Local Radial Basis Function Karel's algorithm (KAREL), for interpolation problems. The research focuses on three challenging applications: Franke's function in two and three dimensions, and grayscale image reconstruction. All three schemes, operating in a local interpolation manner, are assessed across multiple criteria, including accuracy, CPU time and storage, and sensitivity to parameters and node sizes. The numerical experiments conducted reveal that while all three schemes yield reasonably good results in most scenarios, the proposed LE-RBF method stands out for its higher accuracy, reduced sensitivity to nodes and shape choices, and lower CPU time and storage requirements. Notably, LERBF demonstrates superior performance in various node densities and shape parameter-selecting strategies, especially when combined with specific strategies like the Carlson shape at 142x142 nodes. Its efficiency in processing time further highlights its practicality for complex applications. The study concludes that LE-RBF, with its robust performance and flexibility, presents a promising avenue for future application in diverse scientific and engineering tasks.