Abstract
For the Hardy classes of functions analytic in the strip around real axis of a size 2β, an optimal method of cardinal interpolation has been proposed within the framework of Optimal Recovery [12]. Below this method, based on the Jacobi elliptic functions, is shown to be optimal according to the criteria of Nonparametric Regression and Optimal Design.
In a stochastic non-asymptotic setting, the maximal mean squared error of the optimal interpolant is evaluated explicitly, for all noise levels away from 0. A pivotal role is played by the interference effect, in which the oscillations exhibited by the interpolant’s bias and variance mutually cancel each other. In the limiting case β → ∞, the optimal interpolant converges to the well-knownNyquist–Shannon cardinal series.
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Levit, B. On Optimal Cardinal Interpolation. Math. Meth. Stat. 27, 245–267 (2018). https://doi.org/10.3103/S1066530718040014
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DOI: https://doi.org/10.3103/S1066530718040014
Keywords
- cardinal interpolation
- Optimal Recovery
- Hardy classes
- Jacobi elliptic functions
- infinite Blaschke product
- interference effect
- sinc filter