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Optimal recovery of linear functionals on sets of finite dimension

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Abstract

Suppose that X is a linear space and L 1, …, L n is a system of linearly independent functionals on P, where P ⊂ X is a bounded set of dimension n + 1. Suppose that the linear functional L 0 is defined in X. In this paper, we find an algorithm that recovers the functional L 0 on the set P with the least error among all linear algorithms using the information L 1 f, …, L n f, f ∈ P.

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Authors and Affiliations

  1. Saratov State University, Saratov, Russia

    S. P. Sidorov

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  1. S. P. Sidorov
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Correspondence to S. P. Sidorov.

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Original Russian Text © S. P. Sidorov, 2008, published in Matematicheskie Zametki, 2008, Vol. 84, No. 4, pp. 602–608.

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Sidorov, S.P. Optimal recovery of linear functionals on sets of finite dimension. Math Notes 84, 561–567 (2008). https://doi.org/10.1134/S0001434608090289

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  • DOI: https://doi.org/10.1134/S0001434608090289

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