@article{SM_2007_198_3_a4,
author = {I. V. Oseledets},
title = {Lower bounds for separable approximations of the {Hilbert} kernel},
journal = {Sbornik. Mathematics},
pages = {425--432},
year = {2007},
volume = {198},
number = {3},
language = {en},
url = {http://geodesic.mathdoc.fr/item/SM_2007_198_3_a4/}
}
I. V. Oseledets. Lower bounds for separable approximations of the Hilbert kernel. Sbornik. Mathematics, Tome 198 (2007) no. 3, pp. 425-432. http://geodesic.mathdoc.fr/item/SM_2007_198_3_a4/
[1] A. A. Laptev, “Spektralnaya asimptotika odnogo klassa integralnykh operatorov”, Matem. zametki, 16:5 (1974), 741–750 | MR | Zbl
[2] H. Widom, “Hankel matrices”, Trans. Amer. Math. Soc, 121:1 (1966), 1–35 | DOI | MR | Zbl
[3] E. E. Tyrtyshnikov, “Mosaic-skeleton approximations”, Calcolo, 33:1–2 (1996), 47–57 | DOI | MR | Zbl
[4] S. A. Goreinov, “Mozaichno-skeletonnye approksimatsii matrits, porozhdennykh asimptoticheski gladkimi i ostsilyatsionnymi yadrami”, Matrichnye metody i vychisleniya, IVM RAN, M., 1999, 42–76
[5] W. Hackbusch, B. N. Khoromskii, E. E. Tyrtyshnikov, “Hierarchical Kronecker tensor-product approximations”, J. Numer. Math., 13:2 (2005), 119–156 | DOI | MR | Zbl
[6] D. Braess, W. Hackbusch, “Approximation of $1/x$ by exponential sums in $[1,\infty)$”, IMA J. Numer. Anal, 25:4 (2005), 685–697 | DOI | MR | Zbl
[7] S. A. Goreinov, E. E. Tyrtyshnikov, “The maximal-volume concept in approximation by low-rank matrices”, Structured matrices in mathematics, computer science, and engineering I (Boulder, CO, 1999), Contemp. Math., 280, Amer. Math. Soc., Providence, RI, 2001, 47–51 | MR | Zbl
[8] E. I. Zolotarev, Sobranie sochinenii, t. XXX, vyp. 5, Sankt-Peterbugskaya akademiya nauk, 1877
[9] A. A. Gonchar, “O zadachakh E. I. Zolotareva, svyazannykh s ratsionalnymi funktsiyami”, Matem. sb., 78(120):4 (1969), 640–654 | MR | Zbl
[10] A. A. Medovikov, V. I. Lebedev, “Optimization of $L_\omega$ stable Crank–Nicolson method”, Russian J. Numer. Anal. Math. Modelling, 20:3 (2005), 283–304 | DOI | MR | Zbl