Full C(N)D-study of computational capabilities of Lagrange polynomials
Taugynbayeva G. Azhgaliyev S. Zhubanysheva A. Temirgaliyev N.
January 2025Elsevier B.V.
Mathematics and Computers in Simulation
2025#227189 - 208 pp.
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.
Computational (numerical) diameter , Lagrange interpolation polynomials , Lagrange spline , Limiting error , Optimal recovery , Recovery of function by accurate and inaccurate information
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Institute of Theoretical Mathematics and Scientific Computations, L. N. Gumilyov Eurasian National University, Satpayev Str., 2, Astana, 010008, Kazakhstan
Institute of Theoretical Mathematics and Scientific Computations
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