Bounds for the sampling discretization error and their applications to the universal sampling discretization

2023/12/09 by Kosov, E. D., Temlyakov, V. N. · 1 citation
#41A63 (Secondary) #65D30 #65J05 (Primary) 42A05 #FOS: Mathematics #Functional Analysis (math.FA) #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.2312.05670

Abstract

In the first part of the paper we study absolute error of sampling discretization of the integral L_p-norm for function classes of continuous functions. We use basic approaches from chaining technique to provide general upper bounds for the error of sampling discretization of the L_p-norm on a given function class in terms of entropy numbers in the uniform norm of this class. As an example we apply these general results to obtain new error bounds for sampling discretization of the L_p-norms on classes of multivariate functions with mixed smoothness. In the second part of the paper we apply our general bounds to study the problem of universal sampling discretization.

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• Sampling and entropy numbers in the uniform norm

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• Sampling discretization error of integral norms for function classes with small smoothness
• Sampling discretization error for function classes
• Universal sampling discretization
• Sampling discretization of integral norms and its application
• Sampling and entropy numbers in the uniform norm