Multivariate Anisotropic Interpolation on the Torus
Ronny Bergmann, J\"urgen Prestin
TL;DR
This paper analyzes the error in periodic interpolation on the torus, generalizing Strang-Fix conditions to anisotropic settings to account for directional smoothness differences, providing bounds on interpolation accuracy.
Contribution
It introduces anisotropic Strang-Fix conditions for periodic interpolation on the torus and derives error bounds considering directional smoothness.
Findings
Derived upper bounds for interpolation error.
Extended Strang-Fix conditions to anisotropic settings.
Accounted for varying smoothness along different directions.
Abstract
We investigate the error of periodic interpolation, when sampling a function on an arbitrary pattern on the torus. We generalize the periodic Strang-Fix conditions to an anisotropic setting and provide an upper bound for the error of interpolation. These conditions and the investigation of the error especially take different levels of smoothness along certain directions into account.
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