6 papers
Spectral Bounds for Kernel Quadrature
A. Cloninger, Q. T. Le Gia, H. N. Mhaskar
A bottleneck in the theory of kernel methods in machine learning is the storage requirement. To ameliorate this, a standard trick is to replace the kernel with an explicit feature…
A simple modification to mitigate locking in conforming FEM for nearly incompressible elasticity
K. Mustapha, W. McLean, J. Dick +1
Due to the divergence-instability, the accuracy of low-order conforming finite element methods (FEMs) for nearly incompressible elasticity equations deteriorates as the Lamé parame…
High-order QMC nonconforming FEMs for nearly incompressible planar stochastic elasticity equations
J. Dick, T. Le Gia, W. McLean +2
In a recent work (Dick et al, arXiv:2310.06187), we considered a linear stochastic elasticity equation with random Lamé parameters which are parameterized by a countably infinite n…
Quasi-Monte Carlo sparse grid Galerkin finite element methods for linear elasticity equations with uncertainties
M. Clarke, J. Dick, Q. T. Le Gia +2
We explore a linear inhomogeneous elasticity equation with random Lamé parameters. The latter are parameterized by a countably infinite number of terms in separated expansions. The…
Removing the mask -- reconstructing a scalar field on the sphere from a masked field
Jan Hamann, Quoc Thong Le Gia, Ian H. Sloan +1
The paper analyses a spectral approach to reconstructing a scalar field on the sphere, given only information about a masked version of the field together with precise information…
Approximation of noisy data using multivariate splines and finite element methods
Elizabeth Harris, Bishnu Lamichhane, Quoc Thong Le Gia
We compare a recently proposed multivariate spline based on mixed partial derivatives with two other standard splines for the scattered data smoothing problem. The splines are defi…