Worst case tractability of linear problems in the presence of noise: linear information

2023/03/28 by Leszek Plaskota, Plaskota, Leszek, Paweł Siedlecki +1 · 1 citation
Computer Science · Decision Sciences · Mathematics · #Advanced Mathematical Modeling in Engineering #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods in inverse problems #Probabilistic and Robust Engineering Design

paper · pdf · doi:10.48550/arxiv.2303.16328

openalex publication_date 2023/03/28 · openalex created_date 2023/04/05 · openalex updated_date 2026/07/28

Abstract

We study the worst case tractability of multivariate linear problems defined on separable Hilbert spaces. Information about a problem instance consists of noisy evaluations of arbitrary bounded linear functionals, where the noise is either deterministic or random. The cost of a single evaluation depends on its precision and is controlled by a cost function. We establish mutual interactions between tractability of a problem with noisy information, the cost function, and tractability of the same problem, but with exact information.

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• Noisy nonlinear information and entropy numbers

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