Full C(N)D-study of computational capabilities of Lagrange polynomials

Galiya Taugynbayeva, Shapen Azhgaliyev, Aksaule Zhubanysheva and Nurlan Temirgaliyev

Mathematics and Computers in Simulation (MATCOM), 2025, vol. 227, issue C, 189-208

Abstract: In the article is determined the exact order of limiting error of inaccurate information in the problem of recovery functions from Sobolev classes according to the information received from all possible linear functionals. The speed of recovery is the same as for accurate information, although this property is lost when we multiply the limiting error for the any increasing sequence. As a consequence of this result, in the context of the Computational (numerical) diameter, it is shown that Lagrange spline interpolation is the most effective among all possible computing methods, according to the information by value at points. Computational experiments confirm this conclusion.

Keywords: Recovery of function by accurate and inaccurate information; Computational (numerical) diameter; Optimal recovery; Limiting error; Lagrange interpolation polynomials; Lagrange spline (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:227:y:2025:i:c:p:189-208

DOI: 10.1016/j.matcom.2024.07.032

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