期刊
APPLIED MATHEMATICS AND COMPUTATION
卷 377, 期 -, 页码 -出版社
ELSEVIER SCIENCE INC
DOI: 10.1016/j.amc.2020.125159
关键词
-
资金
- Hong Kong Research Grant Council GRF Grants
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. (C) 2020 Elsevier Inc. All rights reserved.
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