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Optimal Recovery Methods Exact on Trigonometric Polynomials for the Solution of the Heat Equation

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Abstract

We consider the problem of the optimal recovery of solutions of the heat equation on the torus \(\mathbb T\) from a finite set of inaccurate Fourier coefficients of the initial temperature. In addition, accuracy conditions on subspaces of trigonometric polynomials of fixed degree are imposed on these methods.

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Authors and Affiliations

  1. National Research University “Moscow Power Engineering Institute”, Moscow, 111250, Russia

    S. A. Unuchek

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  1. S. A. Unuchek
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Correspondence to S. A. Unuchek.

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Translated from Matematicheskie Zametki, 2023, Vol. 113, pp. 118–131 https://doi.org/10.4213/mzm13563.

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Unuchek, S.A. Optimal Recovery Methods Exact on Trigonometric Polynomials for the Solution of the Heat Equation. Math Notes 113, 116–128 (2023). https://doi.org/10.1134/S0001434623010121

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  • DOI: https://doi.org/10.1134/S0001434623010121

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