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Mat. Sb. (N.S.), 1978, Volume 105(147), Number 4, Pages 512–524 (Mi msb2537)  

This article is cited in 66 scientific papers (total in 67 papers)

On Markov's theorem for multipoint Padé approximants

A. A. Gonchar, G. López Lagomasino

Abstract: We study the degree of convergence of interpolating sequences of rational functions (with free poles) for functions of the form $\widehat\mu=\mu*\frac1z$, where $\mu$ is a positive measure with compact support on the real line.
Bibliography: 11 titles.

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English version:
Mathematics of the USSR-Sbornik, 1978, 34:4, 449–459

Bibliographic databases:

UDC: 517.53
MSC: 30E10
Received: 17.11.1977

Citation: A. A. Gonchar, G. López Lagomasino, “On Markov's theorem for multipoint Padé approximants”, Mat. Sb. (N.S.), 105(147):4 (1978), 512–524; Math. USSR-Sb., 34:4 (1978), 449–459

Citation in format AMSBIB
\by A.~A.~Gonchar, G.~L\'opez Lagomasino
\paper On Markov's theorem for multipoint Pad\'e approximants
\jour Mat. Sb. (N.S.)
\yr 1978
\vol 105(147)
\issue 4
\pages 512--524
\jour Math. USSR-Sb.
\yr 1978
\vol 34
\issue 4
\pages 449--459

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    This publication is cited in the following articles:
    1. G. López Lagomasino, “Conditions for convergence of multipoint Padé approximants for functions of Stieltjes type”, Math. USSR-Sb., 35:3 (1979), 363–376  mathnet  crossref  mathscinet  zmath  isi
    2. G. L. Lopes, “On the convergence of the Padé approximants for meromorphic functions of Stieltjes type”, Math. USSR-Sb., 39:2 (1981), 281–288  mathnet  crossref  mathscinet  zmath  isi
    3. Andersson J., “Optimal Quadrature of Hp Functions”, Math. Z., 172:1 (1980), 55–62  crossref  mathscinet  zmath  isi
    4. Prokhorov V., “Tschebyschev Rational-Approximations of Analytic-Functions”, Dokl. AN SSSR, 276:6 (1984), 1321–1324  mathnet  isi
    5. G. L. Lopes, “On the asymptotics of the ratio of orthogonal polynomials and convergence of multipoint Padé approximants”, Math. USSR-Sb., 56:1 (1987), 207–219  mathnet  crossref  mathscinet  zmath
    6. Pineirodiaz L., “The Convergence of Simultaneous Multipoint Approximations”, Vestn. Mosk. Univ. Seriya 1 Mat. Mekhanika, 1986, no. 3, 88–91  mathscinet  zmath  isi
    7. Stahl H., “Orthogonal Polynomials with Complex-Valued Weight Function .1.”, Constr. Approx., 2:3 (1986), 225–240  crossref  mathscinet  zmath  isi
    8. 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
    9. G. L. Lopes, “Relative asymptotics for polynomials orthogonal on the real axis”, Math. USSR-Sb., 65:2 (1990), 505–529  mathnet  crossref  mathscinet  zmath
    10. Lopez G., Rakhmanov E., “Rational-Approximations, Orthogonal Polynomials and Equilibrium Distributions”, Lect. Notes Math., 1329 (1988), 125–157  crossref  mathscinet  zmath  isi
    11. Herbert Stahl, “On the convergence of generalized Padé approximants”, Constr Approx, 5:1 (1989), 221  crossref  mathscinet  zmath  isi
    12. Guillermo López Lagomasino, “Asymptotics of polynomials orthogonal with respect to varying measures”, Constr Approx, 5:1 (1989), 199  crossref  mathscinet  zmath  isi
    13. K. Pan, “On orthogonal systems of rational functions on the unit circle and polynomials orthogonal with respect to varying measures”, Journal of Computational and Applied Mathematics, 47:3 (1993), 313  crossref
    14. 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
    15. Stahl H., “Best Uniform Rational Approximation of X-Alpha on [0, 1]”, Bull. Amer. Math. Soc., 28:1 (1993), 116–122  crossref  mathscinet  zmath  isi
    16. A. Martínez, A. Sarso, R. Yan'es, “Two approaches to the asymptotics of the zeros of a class of hypergeometric-type polynomials”, Russian Acad. Sci. Sb. Math., 83:2 (1995), 483–494  mathnet  crossref  mathscinet  zmath  isi
    17. K. Pan, “On the convergence of the rational interpolation approximant of Carathéodory functions”, Journal of Computational and Applied Mathematics, 54:3 (1994), 371  crossref
    18. K. Pan, “On the orthogonal rational functions with arbitrary poles and interpolation properties”, Journal of Computational and Applied Mathematics, 60:3 (1995), 347  crossref
    19. Vilmos Totik, “Orthogonal polynomials with respect to varying weights”, Journal of Computational and Applied Mathematics, 99:1-2 (1998), 373  crossref
    20. Hernandez M. Lagomasino G., “Ratio and Relative Asymptotics of Polynomials Orthogonal on an Arc of the Unit Circle”, J. Approx. Theory, 92:2 (1998), 216–244  crossref  mathscinet  zmath  adsnasa  isi
    21. Alexei Zhedanov, “Biorthogonal Rational Functions and the Generalized Eigenvalue Problem”, Journal of Approximation Theory, 101:2 (1999), 303  crossref
    22. 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
    23. F Wielonsky, “Rational Approximation to the Exponential Function with Complex Conjugate Interpolation Points”, Journal of Approximation Theory, 111:2 (2001), 344  crossref
    24. 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
    25. Gautschi W., “The Use of Rational Functions in Numerical Quadrature”, J. Comput. Appl. Math., 133:1-2 (2001), 111–126  crossref  mathscinet  zmath  isi
    26. Ysern B. Lagomasino G., “Convergence of Multipoint Pade-Type Approximants”, J. Approx. Theory, 109:2 (2001), 257–278  crossref  mathscinet  zmath  adsnasa  isi
    27. 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
    28. 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
    29. Druskin V., Moskow S., “Three-Point Finite-Difference Schemes, Pade and the Spectral Galerkin Method. I. One-Sided Impedance Approximation”, Math. Comput., 71:239 (2002), 995–1019  mathscinet  zmath  isi
    30. A. A. Gonchar, “Rational Approximations of Analytic Functions”, Proc. Steklov Inst. Math., 272, suppl. 2 (2011), S44–S57  mathnet  crossref  crossref  mathscinet  zmath  isi
    31. Asvadurov S., Druskin V., Guddati M., Knizhnerman L., “On Optimal Finite-Difference Approximation of Pml”, SIAM J. Numer. Anal., 41:1 (2003), 287–305  crossref  mathscinet  zmath  isi
    32. Hernandez M. Ceniceros J., “Strong Asymptotic Behavior for Extremal Polynomials with Respect to Varying Measures on the Unit Circle”, J. Approx. Theory, 125:1 (2003), 131–144  crossref  zmath  isi
    33. Prieto, UF, “Hermite-Pade approximation and simultaneous quadrature formulas”, Journal of Approximation Theory, 126:2 (2004), 171  crossref  isi
    34. Wielonsky, F, “Riemann–Hilbert analysis and uniform convergence of rational interpolants to the exponential function”, Journal of Approximation Theory, 131:1 (2004), 100  crossref  isi  elib
    35. A. L. Lukashov, “Ratsionalnye interpolyatsionnye protsessy na neskolkikh otrezkakh”, Izv. Sarat. un-ta. Nov. ser. Ser. Matematika. Mekhanika. Informatika, 5:1-2 (2005), 34–48  mathnet
    36. L. Baratchart, F. Mandréa, E.B. Saff, F. Wielonsky, “2-D inverse problems for the Laplacian: A meromorphic approximation approach”, Journal de Mathématiques Pures et Appliquées, 86:1 (2006), 1  crossref
    37. Antonio J. Duran, Mourad E.H. Ismail, “Differential coefficients of orthogonal matrix polynomials”, Journal of Computational and Applied Mathematics, 190:1-2 (2006), 424  crossref
    38. Baratchart L., “A Remark on Uniqueness of Best Rational Approximants of Degree 1 in l-2 of the Circle”, Electron. Trans. Numer. Anal., 25 (2006), 54–66  mathscinet  zmath  isi
    39. U. Fidalgo Prieto, J. R. Illán González, G. López Lagomasino, “Convergence and computation of simultaneous rational quadrature formulas”, Numer Math, 106:1 (2007), 99  crossref  mathscinet  zmath  isi  elib
    40. Prieto U.F. Lopez Lagomasino G., “General Results on the Convergence of Multipoint Hermite-Pade Approximants of Nikishin Systems”, Constr. Approx., 25:1 (2007), 89–107  crossref  mathscinet  zmath  isi
    41. G. López Lagomasino, L. Reichel, L. Wunderlich, “Matrices, moments, and rational quadrature”, Linear Algebra and its Applications, 429:10 (2008), 2540  crossref
    42. 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
    43. A. A. Kandayan, “Multipoint Padé Approximations of the Beta Function”, Math. Notes, 85:2 (2009), 176–189  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    44. Baratchart, L, “Convergent Interpolation to Cauchy Integrals over Analytic Arcs”, Foundations of Computational Mathematics, 9:6 (2009), 675  crossref  isi  elib
    45. Baratchart, L, “Multipoint Pade approximants to complex Cauchy transforms with polar singularities”, Journal of Approximation Theory, 156:2 (2009), 187  crossref  isi
    46. Prokhorov V.A. Putinar M., “Compact Hankel Forms on Planar Domains”, Complex Anal. Oper. Theory, 3:2 (2009), 471–499  crossref  mathscinet  zmath  isi
    47. L. Baratchart, M. L. Yattselev, “Meromorphic approximants to complex Cauchy transforms with polar singularities”, Sb. Math., 200:9 (2009), 1261–1297  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    48. Baratchart L., Yattselev M., “Convergent Interpolation to Cauchy Integrals over Analytic Arcs with Jacobi-Type Weights”, International Mathematics Research Notices, 2010, no. 22, 4211–4275  isi
    49. de la Calle Ysern B., “A Walk through Approximation Theory”, Recent Trends in Orthogonal Polynomials and Approximation Theory, Contemporary Mathematics, 507, 2010, 25–86  crossref  isi
    50. Carl Jagels, Lothar Reichel, “Recursion relations for the extended Krylov subspace method”, Linear Algebra and its Applications, 434:7 (2011), 1716  crossref
    51. Derevyagin M., “The Jacobi matrices approach to Nevanlinna-Pick problems”, J Approx Theory, 163:2 (2011), 117–142  crossref  isi
    52. Rakhmanov E.A., “Orthogonal Polynomials and S-Curves”, Recent Advances in Orthogonal Polynomials, Special Functions, and their Applications, Contemporary Mathematics, 578, eds. Arvesu J., Lagomasino G., Amer Mathematical Soc, 2011, 195–239  crossref  isi
    53. 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
    54. 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
    55. 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
    56. A. I. Aptekarev, “Integriruemye poludiskretizatsii giperbolicheskikh uravnenii – “skhemnaya” dispersiya i mnogomernaya perspektiva”, Preprinty IPM im. M. V. Keldysha, 2012, 020, 28 pp.  mathnet
    57. Lukashov A. Akal C., “Determinant Form and a Test of Convergence for the Newton-Pade Approximations”, J. Comput. Anal. Appl., 15:1 (2013), 55–64  mathscinet  isi
    58. 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
    59. M.S.. Pranić, Lothar Reichel, “Rational Gauss Quadrature”, SIAM J. Numer. Anal, 52:2 (2014), 832  crossref
    60. V.A.. Prokhorov, “On rational approximation of Markov functions on finite sets”, Journal of Approximation Theory, 2014  crossref
    61. A. I. Aptekarev, A. I. Bogolyubskii, “Matrichnaya zadacha Rimana–Gilberta dlya approksimatsii Pade po ortogonalnym razlozheniyam”, Preprinty IPM im. M. V. Keldysha, 2014, 103, 16 pp.  mathnet
    62. Carl Jagels, Lothar Reichel, “On the computation of Gauss quadrature rules for measures with a monomial denominator”, Journal of Computational and Applied Mathematics, 2015  crossref
    63. Martinez-Finkelshtein A., Orive R., Rakhmanov E.A., “Phase Transitions and Equilibrium Measures in Random Matrix Models”, Commun. Math. Phys., 333:3 (2015), 1109–1173  crossref  mathscinet  zmath  isi  elib
    64. 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
    65. A. I. Bogolyubskii, “Strong Asymptotics of Diagonal Frobenius–Padé Approximants and Nikishin Systems”, Math. Notes, 99:6 (2016), 938–941  mathnet  crossref  crossref  mathscinet  isi  elib
    66. 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
    67. Lubinsky D.S., “On Uniform Convergence of Diagonal Multipoint Pade Approximants For Entire Functions”, Constr. Approx., 49:1 (2019), 149–174  crossref  mathscinet  zmath  isi  scopus
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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