64 citations · 175 across the 9 of their papers we have counts for
11 papers
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…
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…
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…
Direct and Inverse Results on Bounded Domains for Meshless Methods via Localized Bases on Manifolds
Thomas Hangelbroek, Francis J. Narcowich, Christian Rieger +1
This article develops direct and inverse estimates for certain finite dimensional spaces arising in kernel approximation. Both the direct and inverse estimates are based on approxi…
A Novel Galerkin Method for Solving PDEs on the Sphere Using Highly Localized Kernel Bases
F. J. Narcowich, Stephen T. Rowe, Joseph D. Ward
We present a novel Galerkin method for solving partial differential equations on the sphere. The problem is discretized by a highly localized basis which is easily constructed. The…
Kernel Based Quadrature on Spheres and Other Homogeneous Spaces
E. Fuselier, T. Hangelbroek, F. J. Narcowich +2
Quadrature formulas for spheres, the rotation group, and other compact, homogeneous manifolds are important in a number of applications and have been the subject of recent research…
Localized bases for kernel spaces on the unit sphere
E. Fuselier, T. Hangelbroek, F. J. Narcowich +2
Approximation/interpolation from spaces of positive definite or conditionally positive definite kernels is an increasingly popular tool for the analysis and synthesis of scattered…
Polyharmonic and Related Kernels on Manifolds: Interpolation and Approximation
T. Hangelbroek, F. J. Narcowich, J. D. Ward
This article is devoted to developing a theory for effective kernel interpolation and approximation in a general setting. For a wide class of compact, connected Riemanni…
Cardinal Interpolation with Gaussian Kernels
Thomas Hangelbroek, Wolodymyr Madych, F. J. Narcowich +1
In this paper, interpolation by scaled multi-integer translates of Gaussian kernels is studied. The main result establishes Sobolev error estimates and shows that the error i…
Kernel Approximation on Manifolds I: Bounding the Lebesgue Constant
Thomas Hangelbroek, Fran J. Narcowich, Joe D. Ward
The purpose of this paper is to establish that for any compact, connected C^{\infty} Riemannian manifold there exists a robust family of kernels of increasing smoothness that are w…
L^p Bernstein estimates and approximation by spherical basis functions
H. N. Mhaskar, F. J. Narcowich, J. Prestin +1
The purpose of this paper is to establish L^p error estimates, a Bernstein inequality, and inverse theorems for approximation by a space comprising spherical basis functions locate…