Geodesic
Example of Divergence of a Greedy Algorithm with Respect to an Asymmetric Dictionary
Matematičeskie zametki, Tome 109 (2021) no. 3, pp. 352-360

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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 inner product with the elements of $D$ (not the modulus of this inner product) is maximized at each step, diverges for some initial element.
Keywords: Hilbert space, greedy approximations, asymmetric dictionary
Mots-clés : convergence. 
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     author = {P. A. Borodin},
     title = {Example of {Divergence} of a {Greedy} {Algorithm} with {Respect} to an {Asymmetric} {Dictionary}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {352--360},
     publisher = {mathdoc},
     volume = {109},
     number = {3},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2021_109_3_a2/}
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P. A. Borodin. Example of Divergence of a Greedy Algorithm with Respect to an Asymmetric Dictionary. Matematičeskie zametki, Tome 109 (2021) no. 3, pp. 352-360. http://geodesic.mathdoc.fr/item/MZM_2021_109_3_a2/