Geodesic
Kolmogorov width and approximate rank
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Harmonic analysis, approximation theory, and number theory, Tome 303 (2018), pp. 155-168

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Closely related notions of the Kolmogorov width and the approximate rank of a matrix are considered. New estimates are established in approximation problems related to the width of the set of characteristic functions of intervals; the multidimensional case (characteristic functions of parallelepipeds) is also considered. 
@article{TM_2018_303_a11,
     author = {B. S. Kashin and Yu. V. Malykhin and K. S. Ryutin},
     title = {Kolmogorov width and approximate rank},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {155--168},
     publisher = {mathdoc},
     volume = {303},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2018_303_a11/}
}
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B. S. Kashin; Yu. V. Malykhin; K. S. Ryutin. Kolmogorov width and approximate rank. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Harmonic analysis, approximation theory, and number theory, Tome 303 (2018), pp. 155-168. http://geodesic.mathdoc.fr/item/TM_2018_303_a11/