3 papers
math.NA2018
Interpolating splines on graphs for data science applications
John Paul Ward, Francis J. Narcowich, Joseph D. Ward
We introduce intrinsic interpolatory bases for data structured on graphs and derive properties of those bases. Polyharmonic Lagrange functions are shown to satisfy exponential deca…
math.NA2016
A Meshless Galerkin Method For Non-Local Diffusion Using Localized Kernel Bases
Richard B. Lehoucq, Francis J. Narcowich, Stephen T. Rowe +1
We introduce a meshless method for solving both continuous and discrete variational formulations of a volume constrained, nonlocal diffusion problem. We use the discrete solution t…
math.NA2015
An inverse theorem for compact Lipschitz regions in using localized kernel bases
Thomas Hangelbroek, Francis J. Narcowich, Christian Rieger +1
While inverse estimates in the context of radial basis function approximation on boundary-free domains have been known for at least ten years, such theorems for the more important…