The problem of optimal extrapolation of polynomials given with an error on a compact set is studied. Its relationship with Chebyshev’s problem on a polynomial that least deviates from zero on a compact set is established. An exact solution to the problem of optimal extrapolation of polynomials is obtained for the case when the compact set is a lemniscate. An exact solution is written for the problem of extrapolation from the interval [-1, 1] to the real line.
Keywords: optimal extrapolation of polynomials, optimal recovery of functionals, Chebyshev polynomial of a compact set
Received April 21, 2024
Revised October 16, 2024
Accepted November 5, 2024
Alexey Andreevich Trembach, Krasovskii Institute of Mathematics and Mechanics of the Ural Branch of the Russian Academy of Sciences, Yekaterinburg, 620108 Russia, e-mail: alex.trembach2015@yandex.ru
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Cite this article as: A.A. Trembach. Optimal extrapolation of polynomials given with error. Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2024, vol. 30, no. 4, pp. 265–275.
