Document Type

Journal Article

Department/Unit

Department of Mathematics

Language

English

Abstract

This work focuses on the invertibility of non-constant shape Gaussian asymmetric interpolation matrix, which includes the cases of both variable and random shape parameters. We prove a sufficient condition for that these interpolation matrices are invertible almost surely for the choice of shape parameters. The proof is then extended to the case of anisotropic Gaussian kernels, which is subjected to independent componentwise scalings and rotations. As a corollary of our proof, we propose a parameter free random shape parameters strategy to completely eliminate the need of users’ inputs. By studying numerical accuracy in variable precision computations, we demonstrate that the asymmetric interpolation method is not a method with faster theoretical convergence. We show empirically in double precision, however, that these spatially varying strategies have the ability to outperform constant shape parameters in double precision computations. Various random distributions were numerically examined.

Publication Date

7-15-2020

Source Publication Title

Applied Mathematics and Computation

Volume

377

Publisher

Elsevier

DOI

10.1016/j.amc.2020.125159

Link to Publisher's Edition

https://doi.org/10.1016/j.amc.2020.125159

ISSN (print)

00963003

Available for download on Monday, August 01, 2022

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