Near-optimality of Σ quantization for L2-approximation with polynomials in Bernstein form

C. Sinan Gunturk; Weilin Li

doi:10.1109/SampTA59647.2023.10301376

Near-optimality of Σ quantization for L²-approximation with polynomials in Bernstein form

C. Sinan Gunturk, Weilin Li

Mathematics

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Abstract

In this paper, we provide lower bounds on the L²-error of approximation of arbitrary functions f : [0, 1] → R by polynomials of degree at most n, with the constraint that the coefficients of these polynomials in the Bernstein basis of order n are bounded by n^α for some α ≥ 0. For Lipschitz functions, this lower bound matches, up to a factor of n , a previously obtained constructive upper bound for the error of approximation by one-bit polynomials in Bernstein form via Σ quantization where the functions are bounded by 1 and the coefficients of the approximating polynomials are constrained to be in ±1.

Original language	English (US)
Title of host publication	2023 International Conference on Sampling Theory and Applications, SampTA 2023
Publisher	Institute of Electrical and Electronics Engineers Inc.
ISBN (Electronic)	9798350328851
DOIs	https://doi.org/10.1109/SampTA59647.2023.10301376
State	Published - 2023
Event	2023 International Conference on Sampling Theory and Applications, SampTA 2023 - New Haven, United States Duration: Jul 10 2023 → Jul 14 2023

Publication series

Name	2023 International Conference on Sampling Theory and Applications, SampTA 2023

Conference

Conference	2023 International Conference on Sampling Theory and Applications, SampTA 2023
Country/Territory	United States
City	New Haven
Period	7/10/23 → 7/14/23

ASJC Scopus subject areas

Discrete Mathematics and Combinatorics
Statistics and Probability
Artificial Intelligence
Computational Theory and Mathematics
Computer Science Applications
Signal Processing

Access to Document

10.1109/SampTA59647.2023.10301376

Cite this

Gunturk, C. S., & Li, W. (2023). Near-optimality of Σ quantization for L²-approximation with polynomials in Bernstein form. In 2023 International Conference on Sampling Theory and Applications, SampTA 2023 (2023 International Conference on Sampling Theory and Applications, SampTA 2023). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/SampTA59647.2023.10301376

Near-optimality of Σ quantization for L²-approximation with polynomials in Bernstein form. / Gunturk, C. Sinan; Li, Weilin.
2023 International Conference on Sampling Theory and Applications, SampTA 2023. Institute of Electrical and Electronics Engineers Inc., 2023. (2023 International Conference on Sampling Theory and Applications, SampTA 2023).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Gunturk, CS & Li, W 2023, Near-optimality of Σ quantization for L²-approximation with polynomials in Bernstein form. in 2023 International Conference on Sampling Theory and Applications, SampTA 2023. 2023 International Conference on Sampling Theory and Applications, SampTA 2023, Institute of Electrical and Electronics Engineers Inc., 2023 International Conference on Sampling Theory and Applications, SampTA 2023, New Haven, United States, 7/10/23. https://doi.org/10.1109/SampTA59647.2023.10301376

Gunturk CS, Li W. Near-optimality of Σ quantization for L²-approximation with polynomials in Bernstein form. In 2023 International Conference on Sampling Theory and Applications, SampTA 2023. Institute of Electrical and Electronics Engineers Inc. 2023. (2023 International Conference on Sampling Theory and Applications, SampTA 2023). doi: 10.1109/SampTA59647.2023.10301376

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