Abstract
We construct an example of an asymmetric dictionary \(D\) in a Hilbert space \(H\) such that the linear combinations of elements of \(D\) with positive coefficients are dense in \(H\), but the greedy algorithm with respect to \(D\), in which the inner product with elements of \(D\) (not the modulus of this inner product) is maximized at each step, diverges for some initial element.
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Translated from Matematicheskie Zametki, 2021, Vol. 109, pp. 352-360 https://doi.org/10.4213/mzm12577.
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Borodin, P.A. Example of Divergence of a Greedy Algorithm with Respect to an Asymmetric Dictionary. Math Notes 109, 379–385 (2021). https://doi.org/10.1134/S0001434621030056
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DOI: https://doi.org/10.1134/S0001434621030056