ORIGINAL RESEARCH article
Front. Appl. Math. Stat.
Sec. Mathematics of Computation and Data Science
Volume 11 - 2025 | doi: 10.3389/fams.2025.1641597
Research on Error Control Method for Polynomial Approximation Based on Equal Amplitude Oscillation Theorem
Provisionally accepted
Letong Zhou1*
Liguo Zhao2- 1University of Warwick, Coventry, United Kingdom
- 2Luoyang Institute of Science and Technology, Luoyang, China
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To address the issue that polynomial approximation methods strongly depend on the analytical form of the objective function, this study proposes a new minimax polynomial approximation method based on the Chebyshev equioscillation theorem. It constructs near-optimal solutions through discrete sample points, introduces a threshold relaxation strategy to locate equioscillation points, and establishes a coefficient solution framework based on linear equations. Experiments cover both noiseless and noisy data scenarios. Compared with methods such as the Least Squares Method (LSM), the results show that the maximum absolute error of the proposed method is effectively reduced, and it performs excellently under different data densities and distributions. This can provide theoretical support for extreme deviation suppression in engineering fields, especially in safety-critical systems.
Keywords: polynomial approximation, Equal amplitude oscillation theorem, minimax optimization, Error control theory, algorithm
Received: 10 Jun 2025; Accepted: 05 Aug 2025.
Copyright: © 2025 Zhou and Zhao. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.
* Correspondence: Letong Zhou, University of Warwick, Coventry, United Kingdom
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