On variable and random shape Gaussian interpolations

Sung Nok CHIU*, Leevan LING, Michael McCourt

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish
Article number125159
JournalApplied Mathematics and Computation
Volume377
DOIs
Publication statusPublished - 15 Jul 2020

Scopus Subject Areas

  • Computational Mathematics
  • Applied Mathematics

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