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Mat. Sb. (N.S.), 1978, Volume 105(147), Number 2, Pages 147–163 (Mi msb2520)  

This article is cited in 41 scientific papers (total in 42 papers)

On the speed of rational approximation of some analytic functions

A. A. Gonchar


Abstract: The speed of rational approximation of functions of the form $\widehat\mu=\mu*(1/z)$ is studied, where $\mu$ is a finite positive measure with compact support, lying on the real line $\mathbf R$.
Bibliography: 11 titles.

Full text: PDF file (1537 kB)
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English version:
Mathematics of the USSR-Sbornik, 1978, 34:2, 131–145

Bibliographic databases:

UDC: 517.53
MSC: Primary 30E10; Secondary 30D50
Received: 23.06.1977

Citation: A. A. Gonchar, “On the speed of rational approximation of some analytic functions”, Mat. Sb. (N.S.), 105(147):2 (1978), 147–163; Math. USSR-Sb., 34:2 (1978), 131–145

Citation in format AMSBIB
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\by A.~A.~Gonchar
\paper On the speed of rational approximation of some analytic functions
\jour Mat. Sb. (N.S.)
\yr 1978
\vol 105(147)
\issue 2
\pages 147--163
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\mathscinet{http://www.ams.org/mathscinet-getitem?mr=489648}
\zmath{https://zbmath.org/?q=an:0374.30029|0407.30027}
\transl
\jour Math. USSR-Sb.
\yr 1978
\vol 34
\issue 2
\pages 131--145
\crossref{https://doi.org/10.1070/SM1978v034n02ABEH001152}
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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. A. A. Gonchar, G. López Lagomasino, “On Markov's theorem for multipoint Padé approximants”, Math. USSR-Sb., 34:4 (1978), 449–459  mathnet  crossref  mathscinet  zmath  isi
    2. Andersson J., “Optimal Quadrature of Hp Functions”, Math. Z., 172:1 (1980), 55–62  crossref  mathscinet  zmath  isi
    3. Prokhorov V., “Tschebyschev Rational-Approximations of Analytic-Functions”, 276, no. 6, 1984, 1321–1324  mathscinet  zmath  isi
    4. Gonchar A., “Rational Approximation of Analytic-Functions”, 1043, 1984, 471–474  isi
    5. Dietrich Braess, “Rational approximation of Stieltjes functions by the Carathéodory-Fejér method”, Constr Approx, 3:1 (1987), 43  crossref  mathscinet  zmath  isi
    6. 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
    7. Goncar A., Rakhmanov E., “On the Rate of Rational Approximation of Analytic-Functions”, Lect. Notes Math., 1354 (1988), 25–42  crossref  mathscinet  isi
    8. V. A. Prokhorov, “Rational approximation of analytic functions”, Russian Acad. Sci. Sb. Math., 78:1 (1994), 139–164  mathnet  crossref  mathscinet  zmath  isi
    9. J. Bustamante, G. López Lagomasino, “Rate of convergence of Hermite-Padé approximants to a Nikishin-type system of analytic functions”, Journal of Computational and Applied Mathematics, 49:1-3 (1993), 19  crossref
    10. Braess D. Lubinsky D. Saff E., “Behavior of Alternation Points in Best Rational Approximation”, Acta Appl. Math., 33:2-3 (1993), 195–210  crossref  mathscinet  zmath  isi
    11. Pan K., “On Orthogonal Systems of Rational Functions on the Unit-Circle and Polynomials Orthogonal with Respect to Varying Measures”, J. Comput. Appl. Math., 47:3 (1993), 313–322  crossref  mathscinet  zmath  isi
    12. Totik V., “Distribution of Simple Zeros of Polynomials”, Acta Math., 170:1 (1993), 1–28  crossref  mathscinet  zmath  isi
    13. V. A. Prokhorov, “On the degree of rational approximation of meromorphic functions”, Russian Acad. Sci. Sb. Math., 81:1 (1995), 1–20  mathnet  crossref  mathscinet  zmath  isi
    14. Andersson J., “Bet Rational Approximation to Markov Functions”, J. Approx. Theory, 76:2 (1994), 219–232  crossref  mathscinet  zmath  isi
    15. A. P. Bulanov, “Rational approximation of functions of several variables with finite Hardy variation”, Sb. Math., 186:11 (1995), 1599–1620  mathnet  crossref  mathscinet  zmath  isi
    16. A. A. Pekarskii, E. A. Rovba, “Uniform approximations of Stieltjes functions by means of an orthoprojection onto the set of rational functions”, Math. Notes, 65:3 (1999), 302–307  mathnet  crossref  crossref  mathscinet  zmath  isi
    17. Alexei Zhedanov, “Biorthogonal Rational Functions and the Generalized Eigenvalue Problem”, Journal of Approximation Theory, 101:2 (1999), 303  crossref
    18. Prokhorov V., Staff E., “Rates of Best Uniform Rational Approximation of Analytic Functions by Ray Sequences of Rational Functions”, Constr. Approx., 15:2 (1999), 155–173  crossref  mathscinet  zmath  isi
    19. L Baratchart, H Stahl, F Wielonsky, “Asymptotic Error Estimates for L2 Best Rational Approximants to Markov Functions”, Journal of Approximation Theory, 108:1 (2001), 53  crossref
    20. Baratchart L., Prokhorov V., Saff E., “Best Meromorphic Approximation of Markov Functions on the Unit Circle”, Found. Comput. Math., 1:4 (2001), 385–416  mathscinet  zmath  isi
    21. Baratchart L. Stahl H. Wielonsky F., “Asymptotic Uniqueness of Best Rational Approximants of Given Degree to Markov Functions in l-2 of the Circle”, Constr. Approx., 17:1 (2001), 103–138  crossref  mathscinet  zmath  isi
    22. 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
    23. 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
    24. A. A. Gonchar, “Rational Approximations of Analytic Functions”, Proc. Steklov Inst. Math., 272, suppl. 2 (2011), S44–S57  mathnet  crossref  crossref  mathscinet  zmath  isi
    25. V. P. Spiridonov, “Essays on the theory of elliptic hypergeometric functions”, Russian Math. Surveys, 63:3 (2008), 405–472  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    26. 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
    27. 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
    28. A. P. Starovoitov, Yu. A. Labych, “Ratsionalnaya approksimatsiya funktsii Markova, porozhdennykh borelevskimi merami stepennogo tipa”, PFMT, 2009, no. 1(1), 69–73  mathnet
    29. Prokhorov V.A. Putinar M., “Compact Hankel Forms on Planar Domains”, Complex Anal. Oper. Theory, 3:2 (2009), 471–499  crossref  mathscinet  zmath  isi
    30. Bernhard Beckermann, Alexis Gryson, “Extremal Rational Functions on Symmetric Discrete Sets and Superlinear Convergence of the ADI Method”, Constr Approx, 2010  crossref
    31. 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
    32. A. A. Gonchar, E. A. Rakhmanov, S. P. Suetin, “Padé–Chebyshev approximants of multivalued analytic functions, variation of equilibrium energy, and the $S$-property of stationary compact sets”, Russian Math. Surveys, 66:6 (2011), 1015–1048  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    33. Maxim Derevyagin, “The Jacobi matrices approach to Nevanlinna–Pick problems”, Journal of Approximation Theory, 163:2 (2011), 117  crossref
    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. Rakhmanov E.A., “Orthogonal Polynomials and S-Curves”, Recent Advances in Orthogonal Polynomials, Special Functions, and their Applications, Contemporary Mathematics, 578, ed. Arvesu J. Lagomasino G., Amer Mathematical Soc, 2011, 195–239  crossref  isi
    36. A. I. Aptekarev, D. N. Tulyakov, “Asymptotics of Meixner polynomials and Christoffel-Darboux kernels”, Trans. Moscow Math. Soc., 73 (2012), 67–106  mathnet  crossref  mathscinet  zmath  elib
    37. A. I. Aptekarev, “Integriruemye poludiskretizatsii giperbolicheskikh uravnenii – “skhemnaya” dispersiya i mnogomernaya perspektiva”, Preprinty IPM im. M. V. Keldysha, 2012, 020, 28 pp.  mathnet
    38. Stefan Güttel, “Rational Krylov approximation of matrix functions: Numerical methods and optimal pole selection”, GAMM-Mitteilungen, 36:1 (2013), 8  crossref
    39. E. A. Rakhmanov, S. P. Suetin, “The distribution of the zeros of the Hermite-Padé polynomials for a pair of functions forming a Nikishin system”, Sb. Math., 204:9 (2013), 1347–1390  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    40. Prokhorov V.A., “On Rational Approximation of Markov Functions on Finite Sets”, J. Approx. Theory, 191:SI (2015), 94–117  crossref  isi
    41. Aptekarev A.I. Yattselev M.L., “Padé approximants for functions with branch points — strong asymptotics of Nuttall–Stahl polynomials”, Acta Math., 215:2 (2015), 217–280  crossref  mathscinet  zmath  isi  scopus
    42. E. A. Rakhmanov, “The Gonchar-Stahl $\rho^2$-theorem and associated directions in the theory of rational approximations of analytic functions”, Sb. Math., 207:9 (2016), 1236–1266  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
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