Ochilov, Sherali Baratovich and Khudayberdieva, Oisha Kurbanovna (2026) Differential Identification and Stable Polynomial Reconstruction from Nonuniform Experimental Data: The 5% Criterion, Operator Norm and Iterative Correction. Central Asian Journal of Innovations on Tourism Management and Finance, 7 (4). ISSN 2660-454X

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Abstract

It is not always possible to describe an experimental process in advance by one of the standard analytical functions. Model selection becomes particularly difficult when the measurement points are nonuniformly spaced, the data contain random errors, and the functional form of the process is unknown. A sequential differential identification algorithm based on scaled divided differences is formalized. The model order m is taken as the first order at which the m-th order scaled divided differences satisfy a prescribed relative stability criterion; a polynomial approximation is then reconstructed by integrating the relation y(m) ≈ C. For nonuniform grids, a differential operator matrix Wm is introduced, and the amplification of measurement errors is estimated through its operator norm. A deterministic sufficient stability condition is derived for a general tolerance γ; for γ = 0.05 it takes the form β + ‖Wm‖∞ε0 ≤ |C|/41. An explicit upper bound is also given for the reconstruction error when the function is smooth but not polynomial. A contractive Landweber-type iterative correction is added to damp the computational error of the initial coefficient estimates. A 100,000-run Monte-Carlo test on a nonuniform cubic example confirmed that the theoretical condition is sufficient and conservative. For a nonpolynomial synthetic process, the 5% criterion stopped at the third order and produced a cubic approximation with a range-normalized RMSE (NRMSE) of 0.103%. The results show that differential identification can be studied as a practical model-selection tool for nonuniform experimental data, although noise amplification in high-order numerical differentiation remains its main limitation. The framework does not treat finite differences or Landweber iteration as new; its contribution is the combined identification–stability–reconstruction workflow for nonuniform experimental data.

Item Type:	Article
Uncontrolled Keywords:	Differential identification, divided differences, nonuniform grid, polynomial approximation, numerical stability, operator norm, Monte-Carlo simulation, Landweber iteration
Subjects:	H Social Sciences
Depositing User:	admin eprints
Date Deposited:	04 Nov 2026 07:18
Last Modified:	04 Nov 2026 07:18
URI:	http://eprints.umsida.ac.id/id/eprint/17406

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