Function values are enough for L2-approximation: Part II.

David Krieg; Mario Ullrich

doi:10.1016/j.jco.2021.101569

Function values are enough for L2-approximation: Part II.

David Krieg
, Mario Ullrich

Research output: Contribution to journal › Article › peer-review

Abstract

In the first part we have shown that, for -approximation of functions from a separable Hilbert space in the worst-case setting, linear algorithms based on function values are almost as powerful as arbitrary linear algorithms if the linear widths are square-summable. That is, they achieve the same polynomial rate of convergence. In this sequel, we prove a similar result for separable Banach spaces and other classes of functions.

Original language	English
Article number	101569
Number of pages	14
Journal	Journal of Complexity
Volume	66
Issue number	66, Paper No. 101569
DOIs	https://doi.org/10.1016/j.jco.2021.101569
Publication status	Published - Oct 2021

Fields of science

101002 Analysis
101032 Functional analysis

JKU Focus areas

Digital Transformation

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10.1016/j.jco.2021.101569

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title = "Function values are enough for L2-approximation: Part II.",

abstract = "In the first part we have shown that, for -approximation of functions from a separable Hilbert space in the worst-case setting, linear algorithms based on function values are almost as powerful as arbitrary linear algorithms if the linear widths are square-summable. That is, they achieve the same polynomial rate of convergence. In this sequel, we prove a similar result for separable Banach spaces and other classes of functions.",

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AB - In the first part we have shown that, for -approximation of functions from a separable Hilbert space in the worst-case setting, linear algorithms based on function values are almost as powerful as arbitrary linear algorithms if the linear widths are square-summable. That is, they achieve the same polynomial rate of convergence. In this sequel, we prove a similar result for separable Banach spaces and other classes of functions.

UR - https://www.scopus.com/pages/publications/85104107411

U2 - 10.1016/j.jco.2021.101569

DO - 10.1016/j.jco.2021.101569

M3 - Article

SN - 1090-2708

VL - 66

JO - Journal of Complexity

JF - Journal of Complexity

IS - 66, Paper No. 101569

M1 - 101569

ER -

Function values are enough for L2-approximation: Part II.

Abstract

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