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Approximation of functions: Optimal sampling and complexity
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DOI：10.1017/S0962492925100287.png)
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Abstract
En 中文
We consider the approximation or recovery of functions based on a finite number of function evaluations. This is a well-studied problem in optimal recovery; machine learning and numerical analysis in general; but many fundamental insights were obtained only recently. We discuss different aspects of the information-theoretic limit that appears because of the limited data available; as well as algorithms and sampling strategies that come as close to it as possible.We also discuss (optimal) sampling in a broader sense; allowing other types of measurements that may be nonlinear; adaptive and random; and present several relations between the different settings in the spirit of information-based complexity. We hope that this article will provide both a basic introduction to the subject and a contemporary summary of the current state of research.
Keywords:
65-02
65D15
41-02
41A65
41A45
41A46
46B09
Journal
IF:
11.3
Papers:
89
Citations:
3.4K
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