General information
Latest issue
Forthcoming papers
Impact factor
Guidelines for authors
License agreement
Submit a manuscript

Search papers
Search references

Latest issue
Current issues
Archive issues
What is RSS

Mat. Sb.:

Personal entry:
Save password
Forgotten password?

Mat. Sb. (N.S.), 1969, Volume 78(120), Number 4, Pages 640–654 (Mi msb3575)  

This article is cited in 51 scientific papers (total in 52 papers)

Zolotarev problems connected with rational functions

A. A. Gonchar

Full text: PDF file (1373 kB)
References: PDF file   HTML file

English version:
Mathematics of the USSR-Sbornik, 1969, 7:4, 623–635

Bibliographic databases:

UDC: 517.53
MSC: 26C15, 26A12, 41A20
Received: 16.12.1968

Citation: A. A. Gonchar, “Zolotarev problems connected with rational functions”, Mat. Sb. (N.S.), 78(120):4 (1969), 640–654; Math. USSR-Sb., 7:4 (1969), 623–635

Citation in format AMSBIB
\by A.~A.~Gonchar
\paper Zolotarev problems connected with rational functions
\jour Mat. Sb. (N.S.)
\yr 1969
\vol 78(120)
\issue 4
\pages 640--654
\jour Math. USSR-Sb.
\yr 1969
\vol 7
\issue 4
\pages 623--635

Linking options:

    SHARE: FaceBook Twitter Livejournal

    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. A. A. Gonchar, “A local condition of single-valuedness of analytic functions”, Math. USSR-Sb., 18:1 (1972), 151–167  mathnet  crossref  mathscinet  zmath
    2. Dov Aharonov, Joseph L Walsh, “On the convergence of rational functions of best approximation to a meromorphic function”, Journal of Mathematical Analysis and Applications, 40:2 (1972), 418  crossref
    3. A. A. Gonchar, “On the convergence of Padé approximants”, Math. USSR-Sb., 21:1 (1973), 155–166  mathnet  crossref  mathscinet  zmath
    4. A. A. Gonchar, “The rate of rational approximation and the property of single-valuedness of an analytic function in the neighborhood of an isolated singular point”, Math. USSR-Sb., 23:2 (1974), 254–270  mathnet  crossref  mathscinet  zmath
    5. A. P. Bulanov, “Asymptotic behavior of the least deviations of the function $\operatorname{sgn}x$ from rational functions”, Math. USSR-Sb., 25:2 (1975), 159–176  mathnet  crossref  mathscinet  zmath
    6. L. D. Grigoryan, “Estimates of the norm of the holomorphic components of functions meromorphic in domains with a smooth boundary”, Math. USSR-Sb., 29:1 (1976), 139–146  mathnet  crossref  mathscinet  zmath  isi
    7. A. A. Gonchar, “On the speed of rational approximation of some analytic functions”, Math. USSR-Sb., 34:2 (1978), 131–145  mathnet  crossref  mathscinet  zmath  isi
    8. Pekarskii A., “Rational-Approximations of Absolutely Continuous-Functions with a Derivative From the Orlich Space”, Dokl. Akad. Nauk Belarusi, 24:4 (1980), 301–304  isi
    9. P. M. Tamrazov, “Capacities of condensers. The method of mixing signed measures”, Math. USSR-Sb., 43:1 (1982), 33–62  mathnet  crossref  mathscinet  zmath
    10. A. S. Sadullaev, “Plurisubharmonic measures and capacities on complex manifolds”, Russian Math. Surveys, 36:4 (1981), 61–119  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    11. A. A. Pekarskii, “Rational approximations of absolutely continuous functions with derivative in an Orlicz space”, Math. USSR-Sb., 45:1 (1983), 121–137  mathnet  crossref  mathscinet  zmath
    12. K. Yu. Osipenko, “Heins' problem and optimal extrapolation of analytic functions prescribed with an error”, Math. USSR-Sb., 54:2 (1986), 551–559  mathnet  crossref  mathscinet  zmath
    13. Vladov N., “Exact Asymptotics for the Rational Approximation of Sign(X) in Hausdorff Metric”, 39, no. 7, 1986, 37–40  isi
    14. Helmut Kloke, “Some inequalities for the capacity of plane condensers”, Results. Math, 9:1-2 (1986), 82  crossref
    15. A. A. Gonchar, E. A. Rakhmanov, “Equilibrium distributions and degree of rational approximation of analytic functions”, Math. USSR-Sb., 62:2 (1989), 305–348  mathnet  crossref  mathscinet  zmath  isi
    16. Gerhard Starke, “Optimal Alternating Direction Implicit Parameters for Nonsymmetric Systems of Linear Equations”, SIAM J Numer Anal, 28:5 (1991), 1431  crossref  mathscinet  zmath  isi
    17. A. L. Levin, E. B. Saff, “$L_p$ extensions of Gonchar's inequality for rational functions”, Russian Acad. Sci. Sb. Math., 76:1 (1993), 199–210  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    18. Gerhard Starke, “Near-circularity for the rational Zolotarev problem in the complex plane”, Journal of Approximation Theory, 70:1 (1992), 115  crossref
    19. N. Levenberg, L. Reichel, “A generalized ADI iterative method”, Numer Math, 66:1 (1993), 215  crossref  mathscinet  zmath  isi
    20. Gerhard Starke, “Fejér-Walsh points for rational functions and their use in the ADI iterative method”, Journal of Computational and Applied Mathematics, 46:1-2 (1993), 129  crossref
    21. M.-P. Istace, J.-P. Thiran, “On the Third and Fourth Zolotarev Problems in the Complex Plane”, SIAM J Numer Anal, 32:1 (1995), 249  crossref  mathscinet  zmath  isi
    22. B. Le Bailly, J. P. Thiran, “Optimal Rational Functions for the Generalized Zolotarev Problem in the Complex Plane”, SIAM J Numer Anal, 38:5 (2000), 1409  crossref  mathscinet  zmath  isi
    23. A. A. Bolibrukh, A. G. Vitushkin, V. S. Vladimirov, E. F. Mishchenko, S. P. Novikov, Yu. S. Osipov, A. G. Sergeev, P. L. Ul'yanov, L. D. Faddeev, E. M. Chirka, “Andrei Aleksandrovich Gonchar (on his 70th birthday)”, Russian Math. Surveys, 57:1 (2002), 191–198  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    24. A. I. Aptekarev, “Sharp constants for rational approximations of analytic functions”, Sb. Math., 193:1 (2002), 1–72  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    25. A. A. Gonchar, “Rational Approximations of Analytic Functions”, Proc. Steklov Inst. Math., 272, suppl. 2 (2011), S44–S57  mathnet  crossref  crossref  mathscinet  zmath  isi
    26. A. A. Medovikov, V. I. Lebedev, “Variable time steps optimization of -stable Crank–Nicolson method”, rus j numer anal math mod, 20:3 (2005), 283  crossref  mathscinet  zmath  elib
    27. V. N. Dubinin, S. I. Kalmykov, “A majoration principle for meromorphic functions”, Sb. Math., 198:12 (2007), 1737–1745  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    28. A. L. Lukashov, “Estimates for derivatives of rational functions and the fourth Zolotarev problem”, St. Petersburg Math. J., 19:2 (2008), 253–259  mathnet  crossref  mathscinet  zmath  isi
    29. I. V. Oseledets, “Lower bounds for separable approximations of the Hilbert kernel”, Sb. Math., 198:3 (2007), 425–432  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    30. Leonid Knizhnerman, Vladimir Druskin, Mikhail Zaslavsky, “On Optimal Convergence Rate of the Rational Krylov Subspace Reduction for Electromagnetic Problems in Unbounded Domains”, SIAM J Numer Anal, 47:2 (2009), 953  crossref  isi
    31. Alphonse P. Magnus, “Elliptic Hypergeometric Solutions to Elliptic Difference Equations”, SIGMA, 5 (2009), 038, 12 pp.  mathnet  crossref  mathscinet  zmath
    32. Druskin, V, “SOLUTION OF LARGE SCALE EVOLUTIONARY PROBLEMS USING RATIONAL KRYLOV SUBSPACES WITH OPTIMIZED SHIFTS”, SIAM Journal on Scientific Computing, 31:5 (2009), 3760  crossref  isi
    33. A. I. Aptekarev, V. I. Buslaev, A. Martínez-Finkelshtein, S. P. Suetin, “Padé approximants, continued fractions, and orthogonal polynomials”, Russian Math. Surveys, 66:6 (2011), 1049–1131  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    34. 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  isi
    35. Yu. A. Labych, A. P. Starovoitov, “Priblizhenie nepreryvnykh funktsii ratsionalnymi drobyami Pade–Chebysheva”, PFMT, 2011, no. 1(6), 69–78  mathnet
    36. A. A. Pekarskii, “Approximation to the Function $z^{\alpha}$ by Rational Fractions in a Domain with Zero External Angle”, Math. Notes, 91:5 (2012), 714–724  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    37. S. I. Kalmykov, “Neravenstva dlya modulei ratsionalnykh funktsii”, Dalnevost. matem. zhurn., 12:2 (2012), 231–236  mathnet
    38. A. I. Aptekarev, “Integriruemye poludiskretizatsii giperbolicheskikh uravnenii – “skhemnaya” dispersiya i mnogomernaya perspektiva”, Preprinty IPM im. M. V. Keldysha, 2012, 020, 28 pp.  mathnet
    39. Stefan Güttel, Leonid Knizhnerman, “A black-box rational Arnoldi variant for Cauchy–Stieltjes matrix functions”, Bit Numer Math, 2013  crossref
    40. Stefan Güttel, “Rational Krylov approximation of matrix functions: Numerical methods and optimal pole selection”, GAMM-Mitteilungen, 36:1 (2013), 8  crossref
    41. M.R.. Opmeer, Timo Reis, Winnifried Wollner, “Finite-Rank ADI Iteration for Operator Lyapunov Equations”, SIAM J. Control Optim, 51:5 (2013), 4084  crossref
    42. V. I. Danchenko, “Integral Estimates of Lengths of Level Lines of Rational Functions and Zolotarev's Problem”, Math. Notes, 94:3 (2013), 314–319  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    43. J.E.. Moussa, “Cubic-scaling algorithm and self-consistent field for the random-phase approximation with second-order screened exchange”, J. Chem. Phys, 140:1 (2014), 014107  crossref
    44. Ng, Tsang, “Chebyshev–Blaschke products: Solutions to certain approximation problems and differential equations”, Journal of Computational and Applied Mathematics, 2014  crossref
    45. Stefan Güttel, Beeumen, Karl Meerbergen, Wim Michiels, “NLEIGS: A Class of Fully Rational Krylov Methods for Nonlinear Eigenvalue Problems”, SIAM J. Sci. Comput, 36:6 (2014), A2842  crossref
    46. S. I. Kalmykov, “Asymptotically Sharp Markov-Type Inequalities for Trigonometric and Algebraic Polynomials”, Math. Notes, 98:2 (2015), 331–335  mathnet  crossref  crossref  mathscinet  isi  elib
    47. J. Math. Sci. (N. Y.), 217:1 (2016), 81–90  mathnet  crossref  mathscinet
    48. A. B. Bogatyrev, S. A. Goreinov, S. Yu. Lyamaev, “Analytical approach to multiband filter synthesis and comparison to other approaches”, Problems Inform. Transmission, 53:3 (2017), 260–273  mathnet  crossref  isi  elib
    49. Bogatyrev A.B. Goreinov S.A. Lyamaev S.Yu., “Eflcient Synthesis of Optimal Multiband Filter”, Russ. J. Numer. Anal. Math. Model, 32:4 (2017), 217–223  crossref  mathscinet  zmath  isi  scopus
    50. Beckermann B., Townsend A., “On the Singular Values of Matrices With Displacement Structure”, SIAM J. Matrix Anal. Appl., 38:4 (2017), 1227–1248  crossref  isi
    51. V. I. Danchenko, M. A. Komarov, P. V. Chunaev, “Ekstremalnye i approksimativnye svoistva naiprosteishikh drobei”, Izv. vuzov. Matem., 2018, no. 12, 9–49  mathnet
    52. Beckermann B., Townsend A., “Bounds on the Singular Values of Matrices With Displacement Structure”, SIAM Rev., 61:2 (2019), 319–344  crossref  mathscinet  isi
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
    Number of views:
    This page:867
    Full text:272
    First page:3

    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2020