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Abstract <p>A method for fitting linearly parameterized (in particular, polynomial) functional dependencies from data with interval uncertainty is developed. In many situations, it provides more adequate processing of inaccurate measurement and observation results than traditional probability-theoretic approaches. The proposed method uses the mathematical apparatus of interval analysis and is based on the so-called maximum compatibility principle. It allows one to effectively construct nonlinear functional dependencies in the form of generalized polynomials from interval data that arise both in dependent and independent variables. As a practical example, processing of real data from an aluminothermic process of industrial waste utilization is considered, where the new method demonstrates a noticeable advantage over the conventional least squares method.</p>

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Polynomial Curve Fitting for Data with Interval Uncertainty

  • 期刊论文

  • 发表日期：

    2025年11月1日

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  • S. P. Shary,
  • A. S. Androsov

摘要

Abstract

A method for fitting linearly parameterized (in particular, polynomial) functional dependencies from data with interval uncertainty is developed. In many situations, it provides more adequate processing of inaccurate measurement and observation results than traditional probability-theoretic approaches. The proposed method uses the mathematical apparatus of interval analysis and is based on the so-called maximum compatibility principle. It allows one to effectively construct nonlinear functional dependencies in the form of generalized polynomials from interval data that arise both in dependent and independent variables. As a practical example, processing of real data from an aluminothermic process of industrial waste utilization is considered, where the new method demonstrates a noticeable advantage over the conventional least squares method.