$\mathcal{H}$-inverses for RBF interpolation

Abstract

We consider the interpolation problem for a class of radial basis functions (RBFs) that includes the classical polyharmonic splines (PHS). We show that the inverse of the system matrix for this interpolation problem can be approximated at an exponential rate in the block rank in the $\mathcal{H}$-matrix format if the block structure of the $\mathcal{H}$-matrix arises from a standard clustering algorithm.

References in corpus (5)

• H-matrix approximability of the inverses of FEM matrices
• Existence of $\mathcal{H}$-matrix approximants to the inverses of BEM matrices: the simple-layer operator
• Existence of $\mathcal{H}$-matrix approximants to the inverse of BEM matrices: the hyper-singular integral operator
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• Exponential meshes and $\mathcal{H}$-matrices