Lower bounds for separable approximations of the Hilbert kernel
Sbornik. Mathematics, Tome 198 (2007) no. 3, pp. 425-432 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

Asymptotically best possible lower bounds for separable approximations are obtained for the function $1/(x+y)$. The method used for the derivation of such bounds is based on the generalization of the maximal volume principle for low-rank approximations. Bibliography: 10 titles.
@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/}
}
TY  - JOUR
AU  - I. V. Oseledets
TI  - Lower bounds for separable approximations of the Hilbert kernel
JO  - Sbornik. Mathematics
PY  - 2007
SP  - 425
EP  - 432
VL  - 198
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/SM_2007_198_3_a4/
LA  - en
ID  - SM_2007_198_3_a4
ER  - 
%0 Journal Article
%A I. V. Oseledets
%T Lower bounds for separable approximations of the Hilbert kernel
%J Sbornik. Mathematics
%D 2007
%P 425-432
%V 198
%N 3
%U http://geodesic.mathdoc.fr/item/SM_2007_198_3_a4/
%G en
%F 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