59 citations · 261 across the 8 of their papers we have counts for
8 papers
A Unified Framework for Efficient Kernel and Polynomial Interpolation
M. Belianovich, G. E. Fasshauer, A. Narayan +1
We present a unified interpolation scheme that combines compactly-supported positive-definite kernels and multivariate polynomials. This unified framework generalizes interpolation…
Quasi-interpolation for high-dimensional function approximation
Wenwu Gao, Jiecheng Wang, Zhengjie Sun +1
The paper proposes a general quasi-interpolation scheme for high-dimensional function approximation. To facilitate error analysis, we view our quasi-interpolation as a two-step pro…
A stabilized radial basis-finite difference (RBF-FD) method with hybrid kernels
Pankaj K Mishra, Gregory E Fasshauer, Mrinal K Sen +1
Recent developments have made it possible to overcome grid-based limitations of finite difference (FD) methods by adopting the kernel-based meshless framework using radial basis fu…
A Nonstationary Designer Space-Time Kernel
Michael McCourt, Gregory Fasshauer, David Kozak
In spatial statistics, kriging models are often designed using a stationary covariance structure; this translation-invariance produces models which have numerous favorable properti…
Hybrid Gaussian-cubic radial basis functions for scattered data interpolation
Pankaj K Mishra, Sankar K Nath, Mrinal K Sen +1
Scattered data interpolation schemes using kriging and radial basis functions (RBFs) have the advantage of being meshless and dimensional independent, however, for the data sets ha…
Solving Support Vector Machines in Reproducing Kernel Banach Spaces with Positive Definite Functions
Gregory E. Fasshauer, Fred J. Hickernell, Qi Ye
In this paper we solve support vector machines in reproducing kernel Banach spaces with reproducing kernels defined on nonsymmetric domains instead of the traditional methods in re…
Approximation of Stochastic Partial Differential Equations by a Kernel-based Collocation Method
Igor Cialenco, Gregory E. Fasshauer, Qi Ye
In this paper we present the theoretical framework needed to justify the use of a kernel-based collocation method (meshfree approximation method) to estimate the solution of high-d…
Rate of Convergence and Tractability of the Radial Function Approximation Problem
Gregory E. Fasshauer, Fred J. Hickernell, Henryk Woźniakowski
This article studies the problem of approximating functions belonging to a Hilbert space with an isotropic or anisotropic Gaussian reproducing kernel, $$ K_d(\bx,\bt) = \exp\…