Superconvergence of kernel-based interpolation

Stability of kernel-based interpolation

It is often observed that interpolation based on translates of radial basis functions or non-radial kernels is numerically unstable due to exceedingly large condition of the kernel matrix. But if stability is assessed in function space without considering special bases, this paper proves that kernel–based interpolation is stable. Provided that the data are not too wildly scattered, the L2 or L∞...

Multilevel Sparse Kernel-Based Interpolation

A multilevel kernel-based interpolation method, suitable for moderately high-dimensional function interpolation problems, is proposed. The method, termed multilevel sparse kernelbased interpolation (MLSKI, for short), uses both level-wise and direction-wise multilevel decomposition of structured (or mildly unstructured) interpolation data sites in conjunction with the application of kernel-base...

Superconvergence of the Iterated Degenerate Kernel Method

Superconvergence of Jacobi-Gauss-Type Spectral Interpolation

In this paper, we extend the study of superconvergence properties of ChebyshevGauss-type spectral interpolation in [24, SINUM,Vol. 50, 2012] to general Jacobi-Gauss-type interpolation. We follow the same principle as in [24] to identify superconvergence points from interpolating analytic functions, but rigorous error analysis turns out much more involved even for the Legendre case. We address t...

Lagrange Interpolation and Finite Element Superconvergence

Abstract. We consider the finite element approximation of the Laplacian operator with the homogeneous Dirichlet boundary condition, and study the corresponding Lagrange interpolation in the context of finite element superconvergence. For ddimensional Qk-type elements with d ≥ 1 and k ≥ 1, we prove that the interpolation points must be the Lobatto points if the Lagrange interpolation and the fin...