Publications Bernhard Beckermann

Published papers - Submitted papers - Other publications - arxiv - On MathSciNet
Published in Mathematical Journals (refereed):
  1. B. Beckermann, G. Labahn, A.C. Matos: On rational functions without Froissart doublets, To appear in Numer. Math. (2017).
    2. arXiv:1605.00506.
  2. B. Beckermann, A. Townsend: On the singular values of matrices with displacement structure, To appear in SIAM J. Matrix Anal. Applics. (2017).
    3. arXiv:1609.09494.
  3. B. Beckermann, N. Stylianopoulos: Bergman orthogonal polynomials and the Grunsky matrix, To appear in Constr.\ Approx. (2017).
    4. arXiv:1606.00553.
  4. B. Beckermann, A.C. Matos: Algebraic properties of robust Padé approximants, J. Approx. Theory 190 (2015) 91-114.
    5. arXiv:1310.2438.
  5. R. Ragonnet, R. Jumentier, B. Beckermann : Bilan du Travail d'Étude et de Recherche "La marche de l'empereur" à l'Université de Lille 1, MATAPLI 102 (2013) 71-82.
    6. (PDF manuscript)
  6. B. Beckermann, M. Crouzeix: Faber polynomials of matrices for non-convex sets, Jaen J. Approx. 6 (2014) 319-231.
    7. arXiv:1310.1356.
  7. B. Beckermann, D. Kressner, Ch. Tobler: An error analysis of Galerkin projection methods for linear systems with tensor product structure, To appear in SIAM J. Num. Anal. (2014).
    8. (revised PDF manuscript)
  8. B. Beckermann, J. Bustamante, R. Mart\'inez-Cruz, J.-M. Quesada: Gaussian, Lobatto and Radau positive quadrature rules with a prescribed abscissa, Université de Lille 1 (2013). Calcolo 51 (2014) 319-328.
    9. (revised PDF manuscript)
  9. C. Badea, B. Beckermann: Spectral sets. Chapter in the second edition of the Handbook of Linear Algebra, Université de Lille (2013).
    10. arXiv:1302.0546.
  10. B. Beckermann, D. Bessis, L. Perotti, D. Vrinceanu: Computing high precision Matrix Pad\'e approximants, Numerical Algorithms 61 (2012) 189-208.
    11. (PDF manuscript)
  11. B. Beckermann, V. Kalyagine, A.C. Matos, F. Wielonsky: Equilibrium problems for vector potentials with semidefinite interaction matrices and constrained masses, Constr. Approx.37 (2013) 101-134.
    12. arXiv:1105.3088v1.
  12. B. Beckermann, S. Guettel: Superlinear convergence of the rational Arnoldi method for the approximation of matrix functions, Numer. Mathematik 121 (2012), 205-236.
    13. (Revised PDF manuscript)
  13. B. Beckermann : An error analysis for rational Galerkin projection applied to the Sylvester equation, SIAM J. Num. Anal. 49 (2012), 2430-2450.
    14. (revised PDF manuscript)
  14. B. Beckermann, V. Kalyagine, A.C. Matos, F. Wielonsky: How well does the Hermite-Padé approximation smooth the Gibbs phenomenon ? Math. Comp. 80 (2011), 931-958.
    15. (revised PDF manuscript)
  15. B. Beckermann, M. Derevyagin, A. Zhedanov : The linear pencil approach to rational interpolation, J. Approx. Theory 162 (2010) 1322-1346.
    16. (PDF manuscript arXiv:0908.3381v1.)
  16. B. Beckermann, S. Guettel, R. Vandebril : On the convergence of rational Ritz values, SIAM J. Matrix Anal. Applics. 31(2010), 1740--1774.
    17. (revised PDF manuscript)
  17. B. Beckermann, L. Reichel : Error estimation and evaluation of matrix functions via the Faber transform, SIAM J. Num. Anal. 47 (2009), 3849-3883.
    18. (revised PDF manuscript)
  18. B. Beckermann, A. Gryson : Extremal rational functions on symmetric discrete sets and superlinear convergence of the ADI method, Constr. Approx.32 (2010) 393-428.
    19. (revised PDF manuscript)
  19. C. Badea, B. Beckermann, M. Crouzeix : Intersections of several disks of the Riemann sphere as K-spectral sets, Commun. Pure Appl. Anal. 8(2009), no. 1, 37--54.
    20. arXiv:0807.3136v2.
  20. B. Beckermann, G. Labahn, Fraction-Free Computation of Simultaneous Padé Approximants, Proceedings of ISSAC'09 Seoul, ACM Press (2009).
    21. (PDF manuscript)
  21. H. Joulak, B. Beckermann : On Gautschi's conjecture for generalized Gauss-Radau and Gauss-Lobatto formulae, J. Comput. Appl. Math.233(2009) 768-774.
    22. (PDF manuscript)
  22. B. Beckermann, L. Reichel : The Arnoldi process and GMRES for nearly symmetric matrices, SIAM J. Matrix Anal. Applics.30(2008) 102-120.
    23. (revised PDF manuscript) Matlab file for the fast GMRES algorithm.
  23. B. Beckermann, A.C. Matos, F. Wielonsky: Reduction of the Gibbs phenomenon for smooth functions with jumps by the $\epsilon$-algorithm, J. Comput. Appl. Math. 219 (2008), 329-349.
    24. (PDF manuscript)
  24. B. Beckermann, M. Crouzeix : Operators with numerical range in a conic domain, Archiv der Mathematik88 (2007) 547-559.
    25. (revised PDF manuscript)
  25. B. Beckermann, S. Serra Capizzano, On the asymptotic spectrum of Finite Element matrix sequences, SIAM J. Num. Anal. 45(2007) 746-769.
    26. (revised PDF manuscript)
  26. B. Beckermann, G. Golub, G. Labahn : On the numerical condition of a generalized Hankel eigenvalue problem, Numer. Mathematik 106 (2007) 41-68.
    27. (revised PDF manuscript)
  27. B. Beckermann : Discrete orthogonal polynomials and superlinear convergence of Krylov subspace methods in numerical linear algebra, in Orthogonal Polynomials and Special Functions, F. Marcellan, W. Van Assche (Eds.), Lecture Notes in Mathematics 1883, Springer Verlag (2006), 119-185.
    28. (see here)
  28. B. Beckermann, M. Crouzeix : A lenticular version of a von Neumann inequality, Archiv der Mathematik 86 (2006) 352-355.
    29. (PDF manuscript)
  29. B. Beckermann, Image numérique, GMRES et polynômes de Faber, C. R. Acad. Sci. Paris, Ser. I 340(2005) 855-860.
    30. (PDF manuscript)
    Some Matlab files for the computation of the Field-of-value asymptotic factor for GMRES etc: FoV_asymptotic_factor.m, FoV_demo.m (requires the Schwartz-Christoffel toolbox of Toby Driscoll).
  30. B. Beckermann, S.A. Goreinov, E.E. Tyrtyshnikov : Some remarks on the Elman estimate for GMRES, SIAM J. Matrix Anal. Applics. 27(2006) 772-778.
    31. (PDF manuscript )
  31. B. Beckermann, H. Cheng, G. Labahn : Fraction-free Row Reduction of Matrices of Ore Polynomials, J. Symbolic Computation 41 (2006) 513-543.

    32. (Click here for an abstract | Get Postscript manuscript | Get pdf manuscript )
  32. B. Beckermann, J. Coussement, W. Van Assche : Multiple Wilson and Jacobi-Piñeiro polynomials, J. Approx. Theory 132 (2005) 155-181.

    33. (Click here for an abstract | Get Postscript manuscript | Get pdf manuscript )
  33. B. Beckermann, A. Martinez, E. Rakhmanov, F. Wielonsky : Asymptotic upper bounds for the entropy of orthogonal polynomials in the Szego class, J. Math. Physics 45 (2004) 4239-4254.
    (Click here for an abstract | Get Postscript manuscript | Get pdf manuscript )
  34. C. Roland, B. Beckermann, C. Brezinski : Altman's methods revisited, Applicationes Mathematicæ 31 (2004) 353-368.
    (Click here for an abstract | Get Postscript manuscript | Get pdf manuscript )
  35. B. Beckermann, M. Castro, On the determinacy of complex Jacobi matrices, Math. Scand. 95 (2004) 285-298.
    (Click here for an abstract | Get Postscript manuscript | Get pdf manuscript )
  36. B. Beckermann, H. Cheng, G. Labahn : Fraction-free row reduction of matrices of skew polynomials, Proceedings of ISSAC'02 Lille, ACM Press (2002) 8-15.
    (Click here for an abstract | Get Postscript manuscript | Get pdf manuscript )
  37. B. Beckermann, A. Osipov, Some spectral properties of infinite band matrices, Numerical Algorithms 34 (2003) 173-185.
    (Click here for an abstract | Get Postscript manuscript | Get pdf manuscript )
  38. B. Beckermann, G. Labahn, G. Villard : Normal Forms for General Polynomial Matrices, J. Symbolic Computation 41 (2006) 708-737.

    39. (Click here for an abstract | Get Postscript manuscript | Get pdf manuscript )
  39. B. Beckermann, A.B.J. Kuijlaars : Superlinear CG convergence for special right-hand sides, Electr. Trans. Num. Anal. 14 (2002) 1-19.
    (Click here for an abstract | Get Postscript manuscript | Get pdf manuscript )
  40. B. Beckermann, A.B.J. Kuijlaars : On the sharpness of an asymptotic error estimate for Conjugate Gradients, BIT 41 (2001), 856-867.
    (Click here for an abstract | Get Postscript manuscript | Get pdf manuscript )
  41. B. Beckermann, M. Castro, V. Kaliaguine : A recurrence relation connected to the convergence of vector S-fractions, East Journal on Approximations 7 (2001) 287-313.
    (Click here for an abstract | Get Postscript manuscript | Get pdf manuscript )
  42. B. Beckermann, A.B.J. Kuijlaars: Superlinear Convergence of Conjugate Gradients, SIAM J. Num. Anal. 39 (2001) 300-329.

    43. (Click here for an abstract | Get Postscript manuscript | Get pdf manuscript )
  43. B. Beckermann: Complex Jacobi matrices, J. Comput. Appl. Math. 127 (2001) 17-65.

    44. (Click here for an abstract | Get Postscript manuscript | Get pdf manuscript )
  44. B. Beckermann, G. Labahn: Numeric and symbolic computation of problems defined by structured linear systems, Reliable Computing 6 (2000) 365-390.

    45. (Click here for an abstract | Get Postscript manuscript | Get pdf manuscript )
  45. B. Beckermann: The Condition Number of real Vandermonde, Krylov and positive definite Hankel matrices, Numer. Mathematik 85 (2000) 553-577.

    46. (Click here for an abstract | Get Postscript manuscript | Get pdf manuscript )
  46. B. Beckermann, G. Labahn: Fraction-free Computation of Matrix Rational Interpolants and Matrix GCD's, SIAM J. Matrix Anal. Appl. 22 (2000) 114-144.

    47. (Click here for an abstract | Get Postscript manuscript | Get pdf manuscript )
  47. B. Beckermann: On a conjecture of E.A. Rakhmanov, Constructive Approximation 16 (2000) 427-448.

    48. (Click here for an abstract | Get Postscript manuscript | Get pdf manuscript )
  48. B. Beckermann: On the classification of the spectrum of second order difference operators, Mathematische Nachrichten 216 (2000), 45-59.

    49. (Click here for an abstract | Get Postscript manuscript | Get pdf manuscript )
  49. B. Beckermann, G. Labahn, G. Villard: Shifted Normal Forms of Polynomial Matrices, Proceedings of ISSAC'99 Vancouver, ACM Press (1999) 189-196.

    50. (Click here for an abstract | Get Postscript manuscript | Get pdf manuscript )
  50. B. Beckermann: On the convergence of bounded J-fractions on the resolvent set of the corresponding second order difference operator, J. Approx. Theory 99 (1999) 369-408.

    51. (Click here for an abstract | Get Postscript manuscript | Get pdf manuscript )
  51. B. Beckermann, E.B. Saff: The sensitivity of Least Squares Polynomial Approximation, in: Proceedings of a Confererence on Orthogonal Polynomials, Oberwolfach, W.\ Gautschi e.a.\ (eds), Int. Ser. of Num. Math. 131, Birkhäuser, Basel (1999) 1-19.

    52. (Click here for an abstract | Get Postscript manuscript | Get pdf manuscript )
  52. B. Beckermann, E. Bourreau: How to choose modified moments? J. Comput. Appl. Math. 98 (1998) 81-98.

    53. (Click here for an abstract)
  53. B. Beckermann, G. Labahn: When are two numerical polynomials relatively prime? J. Symbolic Computations 26 (1998) 677-689.

    54. (Click here for an abstract)
  54. B. Beckermann, G. Labahn: A fast and numerically stable Euclidean-like algorithm for detecting relatively prime numerical polynomials, J. Symbolic Computations 26 (1998) 691-714.

    55. (Click here for an abstract)
  55. B. Beckermann, S. Cabay, G. Labahn: Fraction-free Computation of Matrix Padé Systems, Proceedings of ISSAC'97 Maui, ACM Press (1997) 125-132.

    56. (Click here for an abstract)
  56. P.R. Graves--Morris, B. Beckermann: The Compass (Star) Identity for Vector-valued Rational Interpolants, Advances in Computational Mathematics 7 (1997) 279-294.

    57. (Click here for an abstract)
  57. B. Beckermann, V. Kaliaguine: The diagonal of the Padé table and the approximation of the Weyl function of second order difference operators, Constructive Approximation 13 (1997) 481-510.

    58. (Click here for an abstract)
  58. B. Beckermann, G. Labahn: Recursiveness in Matrix Rational Interpolation Problems, J. Comput. Appl. Math. 77 (1997) 5-34.

    59. (Click here for an abstract)
  59. B. Beckermann: The stable computation of formal orthogonal polynomials, Numerical Algorithms 11 (1996) 1-23.

    60. (Click here for an abstract)
  60. B. Beckermann, C. Carstensen: QD--type algorithms for the non--normal Newton--Padé Approximation Table, Constructive Approximation 12 (1996) 307-330.

    61. (Click here for an abstract)
  61. B. Beckermann, J. Gilewicz, E. Leopold: Recurrence relations with periodic coefficients and Chebyshev polynomials, Applicationes Mathematicae 23 (1995) 319-323.
  62. G. Labahn, B. Beckermann, S. Cabay: Inversion of Mosaic Hankel Matrices via Matrix Polynomials, Lin. Alg. Applics. 221 (1995) 253-279.
  63. J. Wimp, B. Beckermann, Families of Two-point Padé Approximants and New $4F3$ Identities, SIAM J. Math. Anal. 26 (1995) 761-773.
  64. M. Van Barel, B. Beckermann, A. Bultheel & G. Labahn, Matrix rational interpolation with poles as interpolation points, Nonlinear Numerical Methods and Rational Approximation, (A. Cuyts ed.), Kluwer Academic Publishers, (1994) 137-148.

    65. (Click here for an abstract)
  65. B. Beckermann, J. Gilewicz, V. Kaliaguine: On the definition and block structure of a general table of simultaneous Padé approximants, J. Approx. Theory 77 (1994) 65-73.

    66. (Click here for an abstract)
  66. J. Wimp, B. Beckermann, Some explicit formulas for Pade approximants of ratios of hypergeometric functions, WSSIAA 2 (1992) 427-434.

    67. (Click here for an abstract)
  67. B. Beckermann, G. Mühlbach: A general determinantal identity of Sylvester's type and some applications, Lin. Alg. Applics. 197 (1994) 93-112.

    68. (Click here for an abstract)
  68. B. Beckermann, G. Labahn: A uniform approach for the fast computation of Matrix-type Padé approximants, SIAM J. Matrix Anal. Appl. 15 (1994) 804-823.

    69. (Click here for an abstract)
  69. B. Beckermann, C. Carstensen: A reliable Modification of the Cross Rule for Rational Hermite Interpolation, Numerical Algorithms 3 (1992) 29-44.

    70. (Click here for an abstract)
  70. B. Beckermann, G. Labahn: A uniform approach for Hermite Padé and simultaneous Padé Approximants and their Matrix-type generalizations, Numerical Algorithms 3 (1992) 45-54.

    71. (Click here for an abstract)
  71. B. Beckermann, J. Wimp: Some Dynamically Trivial Mappings, with Applications to the Improvement of Simple Iteration, Computers & Mathematics with applications 24 (1992) 89-97.
  72. S. Cabay, G. Labahn, B. Beckermann: On the Theory and Computation of Non-perfect Padé-Hermite Approximants, J. Comput. Appl. Math. 39 (1992) 295-313.
  73. B. Beckermann, C. Carstensen: Global Identities in the Non-Normal Newton-Padé Approximation table, J. Approx. Theory 74(1993) 199-220.

    74. (Click here for an abstract)
  74. B. Beckermann, A. Neuber, G. Mühlbach: Shanks' transformation revisited, Lin. Alg. Applics. 173 (1992) 191-219.

    75. (Click here for an abstract)
  75. B. Beckermann: A reliable method for computing M-Padé approximants on arbitrary staircases, J. Comput. Appl. Math. 40 (1992) 19-42.

    76. (Click here for an abstract)
  76. B. Beckermann: The Structure of the Singular Solution Table of the M-Pade Approximation Problem, J. Comput. Appl. Math. 32 (1990),3-15.
  77. B. Beckermann: A Connection between the E-Algorithm and the Epsilon-Algorithm, IMACS Transactions on Scientific Computing -'88, Vol. 1.2. Numerical and Applied Mathematics, Volume Editor C. Brezinski.

Submitted:

  1. B. Beckermann, C. Mertens, R. Vandebril: On a fast Arnoldi method for BML matrices (2017).
    2. arXiv:1702.00671.
  2. S.-I. Filip, Y. Nakatsukasa, L.N. Trefethen, B. Beckermann, Rational minimax approximation via adaptive barycentric representations (2017)
    3. arXiv:1705.10132.
  3. B. Beckermann, D. Kressner, M. Schweitzer, Low-rank updates of matrix functions (2017).
    4. arXiv:1707.03045.
  4. B. Beckermann, Th. Helart, On the sharpness of the weighted Bernstein-Walsh inequality, with applications to the superlinear convergence of conjugate gradients (2017).
    5. arXiv:1707.07871.

Other publications:

  1. B. Beckermann: Zur Interpolation mit polynomialen Linearkombinationen beliebiger Funktionen, Dissertationsschrift, Universität Hannover, Januar 1990.
  2. B. Beckermann: On the numerical condition of polynomial bases: Estimates for the Condition Number of Vandermonde, Krylov and Hankel matrices, Habilitationsschrift, Universität Hannover (1996).

    3. (Click here for an abstract | Get Postscript manuscript (*.ps.gz) | Get pdf manuscript )
  3. C. Badea, B. Beckermann, M. Crouzeix : K-spectral sets and intersections of disks of the Riemann sphere, arXiv:0712.0522v1 (2007).
  4. M. Lapik, B. Beckermann: The interval of equilibrium for the constrained energy problem in the presence of an external field, Université de Lille (2006).
    5. (PDF manuscript)
  5. B. Beckermann: A note on the convergence of Ritz values for sequences of matrices, Publication ANO 408, Université de Lille (2000).

    6. (Click here for an abstract | Get Postscript manuscript | Get pdf manuscript | See numerical results )
  6. B. Beckermann: On explicit error bounds for best rational and meromorphic approximation of Markov functions on the unit circle, Publication ANO 430, Université de Lille (2001).

    7. (Click here for an abstract | Get Postscript manuscript | Get pdf manuscript )
  7. B. Beckermann, C. Carstensen: On the Computation of the Non-Normal Rational Hermite-Interpolation Table, Grüne Reihe # 241, Univ. Hannover, 1991.

    8. (Click here for an abstract)
  8. B. Beckermann: Neville pivoting for extrapolation and interpolation with non-regular systems, Technical Paper # CPT-92/P.2714, Centre National de la Recherche Scientifique Luminy (1992).

    9. (Click here for an abstract)
  9. B. Beckermann: Nonsymmetric difference operators and polynomials being orthogonal with respect to rectangular matrix valued measures, Publication ANO 335, Université de Lille (1995).

    10. (Click here for an abstract)
  10. B. Beckermann, G. Labahn, On the fraction-free computation of column-reduced matrix polynomials via FFFG. Publication ANO 436, Université de Lille (2001).

    11. (Click here for an abstract | Get Postscript manuscript | Get pdf manuscript )
Last changes: August 28, 2017
bbecker@math.univ-lille1.fr