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首页> 外文期刊>Journal of complexity >On the power of standard information for tractability for L_2-approximation in the average case setting
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On the power of standard information for tractability for L_2-approximation in the average case setting

机译：On the power of standard information for tractability for L_2-approximation in the average case setting

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摘要

We study multivariate approximation in the average case setting with the error measured in the weighted L-2 norm. We consider algorithms that use standard information Lambda(std) consisting of function values or general linear information Lambda(all) consisting of arbitrary continuous linear functionals. We investigate the equivalences of various notions of algebraic and exponential tractability for Lambda(std) and Lambda(all) for the absolute error criterion, and show that the power of Lambda(std) is the same as that of Lambda(all) for all notions of algebraic and exponential tractability without any condition. Specifically, we solve Open Problems 116-118 and almost solve Open Problem 115 as posed by Novak and Wozniakowski (2012) [25]. (C) 2021 Elsevier Inc. All rights reserved.

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