Distributed Uncertainty Quantification of Kernel Interpolation on
  Spheres
Shao-Bo Lin Xingping Sun Di Wang
For radial basis function (RBF) kernel interpolation of scattered data,
Schaback in 1995 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
terms of handling noisy data from challenging computing environments.