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Mat. Sb., 2007, Volume 198, Number 3, Pages 137–144 (Mi msb1530)  

This article is cited in 12 scientific papers (total in 12 papers)

Lower bounds for separable approximations of the Hilbert kernel

I. V. Oseledets

Institute of Numerical Mathematics, Russian Academy of Sciences

Abstract: 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.

DOI: https://doi.org/10.4213/sm1530

Full text: PDF file (417 kB)
References: PDF file   HTML file

English version:
Sbornik: Mathematics, 2007, 198:3, 425–432

Bibliographic databases:

UDC: 519.6+517.518.8
MSC: Primary 41A46; Secondary 65F30
Received: 16.02.2006

Citation: I. V. Oseledets, “Lower bounds for separable approximations of the Hilbert kernel”, Mat. Sb., 198:3 (2007), 137–144; Sb. Math., 198:3 (2007), 425–432

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Oseledets I., “The integral operator with logarithmic kernel has only one positive eigenvalue”, Linear Algebra Appl., 428:7 (2008), 1560–1564  crossref  mathscinet  zmath  isi  elib  scopus
    2. Druskin V., Knizhnerman L., Zaslavsky M., “Solution of large scale evolutionary problems using rational Krylov subspaces with optimized shifts”, SIAM J. Sci. Comput., 31:5 (2009), 3760–3780  crossref  mathscinet  zmath  isi  elib  scopus
    3. Knizhnerman L., Druskin V., Zaslavsky M., “On optimal convergence rate of the rational Krylov subspace reduction for electromagnetic problems in unbounded domains”, SIAM J. Numer. Anal., 47:2 (2009), 953–971  crossref  mathscinet  zmath  isi  elib  scopus
    4. Druskin V., Lieberman Ch., Zaslavsky M., “On adaptive choice of shifts in rational Krylov subspace reduction of evolutionary problems”, SIAM J. Sci. Comput., 32:5 (2010), 2485–2496  crossref  mathscinet  zmath  isi  elib  scopus
    5. Tyrtyshnikov E., “Tensor ranks for the inversion of tensor-product binomials”, J. Comput. Appl. Math., 234:11 (2010), 3170–3174  crossref  mathscinet  zmath  isi  elib  scopus
    6. Druskin V., Knizhnerman L., Simoncini V., “Analysis of the rational Krylov subspace and ADI methods for solving the Lyapunov equation”, SIAM J. Numer. Anal., 49:5 (2011), 1875–1898  crossref  mathscinet  zmath  isi  elib  scopus
    7. Druskin V., Zaslavsky M., “On convergence of Krylov subspace approximations of time-invariant self-adjoint dynamical systems”, Linear Algebra Appl., 436:10 (2012), 3883–3903  crossref  mathscinet  zmath  isi  elib  scopus
    8. Oseledets I.V., “Constructive representation of functions in low-rank tensor formats”, Constr. Approx., 37:1 (2013), 1–18  crossref  mathscinet  zmath  isi  elib  scopus
    9. Simoncini V., “Analysis of the Rational Krylov Subspace Projection Method for Large-Scale Algebraic Riccati Equations”, SIAM J. Matrix Anal. Appl., 37:4 (2016), 1655–1674  crossref  mathscinet  zmath  isi  scopus
    10. Kordy M., Cherkaev E., Wannamaker P., “Adaptive model order reduction for the Jacobian calculation in inverse multi-frequency problem for Maxwell's equations”, Appl. Numer. Math., 109 (2016), 1–18  crossref  mathscinet  zmath  isi  scopus
    11. Beckermann B. Townsend A., “On the Singular Values of Matrices With Displacement Structure”, SIAM J. Matrix Anal. Appl., 38:4 (2017), 1227–1248  crossref  mathscinet  zmath  isi  scopus
    12. Beckermann B., Townsend A., “Bounds on the Singular Values of Matrices With Displacement Structure”, SIAM Rev., 61:2 (2019), 319–344  crossref  mathscinet  zmath  isi
  • Математический сборник Sbornik: Mathematics (from 1967)
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