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The study aims to explore function approximation through optimal sampling and its computational complexities.

June 20, 2026Acta NumericaOpen Access

Approximation of functions: Optimal sampling and complexity

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The study aims to explore function approximation through optimal sampling and its computational complexities.
Analyzed various algorithms for function approximation based on finite evaluations.
Discussed different sampling strategies, including nonlinear, adaptive, and random measurements.
Explored the information-theoretic limits imposed by limited data.
Identified fundamental insights into the information-theoretic limits of function recovery.
Presented relations between different sampling strategies and their effectiveness.
Outlined current state-of-the-art algorithms that approach optimal recovery.

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This article discusses the approximation of functions using optimal sampling strategies, highlighting insights and algorithms.

Krieg et al. (2026) studied this question.

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