Year: 2025
Type: article
Abstract: For radial basis function (RBF) kernel interpolation of scattered data, Schaback [Adv. Comput. Math. 3 (1995), pp. 251–264] proved that the attainable approximation error and the condition number of the underlying interpolation matrix cannot be made small simultaneously. He referred to this finding as an “uncertainty relation,” an undesirable consequence of which is that RBF kernel interpolation is susceptible to noisy data. In this paper, we propose and study a distributed interpolation method to manage and quantify the uncertainty brought on by interpolating noisy spherical data of non-negligible magnitude. We also present numerical simulation results showing that our method is practical and robust in handling noisy data from challenging computing environments.
Source: Mathematics of Computation
DOI: 10.1090/mcom/4076
Authors: Shao-Bo Lin, Xingping Sun, Di Wang
Institutions: Xi'an Jiaotong University, Missouri State University
Language: English
Subfield: Mechanics of Materials
Field: Engineering
Domain: Physical Sciences
Open Access status: green
Award: G8705841576
OpenAlex ID: W4408334060