RBF Interpolation is a highly ill-conditioned problem. We develop a stable and fast multiresolution method for solving Radial Basis Function interpolation of datasets in 3 dimensions. To our knowledge this is the current state of the art solver for linear and higher order RBF interpolation. Applications include medical imaging, geophics and Kriging (regression). This work is currently being extended to higher dimensions.
Test Case #1: 4th order polynomial interpolation with biharmonic spline.
The color reflects the function value on the node
Performance Wall Clock Times: Test Case #1: O(N * sqrt(N))
A discrete adaptedhierarchical basis solver for radial basis function interpolation, BIT Numerical Mathematics, Springer, July 2012.