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Bernhard Beckermann

Professeur des universités CNU : SECTION 26 - MATHEMATIQUES APPLIQUEES ET APPLICATIONS DES MATHEMATIQUES

Publications

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  1. Bernhard Beckermann, Daniel Kressner, Heather Wilber, Compression properties for large Toeplitz-like matrices, Numer. Algo. 100 (2025) 2041-2067, arXiv:2502.09823

  2. B. Beckermann, A. Matos, Solving singular integral equations with orthogonal rational functions (2024) hal-04402726

  3. B. Beckermann, J. Bisch, R. Luce, On the rational approximation of Markov functions, with applications to the computation of Markov functions of Toeplitz matrices, Numer. Algo. 91 (2022) 109-144, arXiv:2106.05098

  4. B. Beckermann, A. Cortinovis, D. Kressner, M. Schweitzer, Low-rank updates of matrix functions II: Rational Krylov methods, SIAM J. Num. Anal. 59 (2021) 1325-1347, arXiv:2008.11501
  5. B. Beckermann, M. Putinar, E.B. Saff, N. Stylianopoulos, Perturbations of Christoffel-Darboux kernels: detection of outliers, Foundations of Computational Mathematics 21 (2021) 71-124,
    arXiv:1812.06560
  6. B. Beckermann, A. Townsend: Bounds on the Singular Values of Matrices with Displacement Structure, SIAM Review 61 (2019) 319-344. hal-04398552
  7. S.-I. Filip, Y. Nakatsukasa, L.N. Trefethen, B. Beckermann, Rational minimax approximation via adaptive barycentric representations, SIAM J. Sci. Comput. 40(4) (2018), A2427-A2455. arXiv:1705.10132
  8. B. Beckermann, C. Mertens, R. Vandebril: On an economic Arnoldi method for BML matrices, SIAM J. Matrix Anal. Appl. 39(2) (2018), 737-768. arXiv:1702.00671
  9. B. Beckermann, D. Kressner, M. Schweitzer, Low-rank updates of matrix functions, SIAM J. Matrix Anal. Appl. 39(1) (2018), 539-565. arXiv:1707.03045
  10. B. Beckermann, G. Labahn, A.C. Matos: On rational functions without Froissart doublets, Numer. Math. 138 (2018) 615-633. arXiv:1605.00506
  11. B. Beckermann, N. Stylianopoulos: Bergman orthogonal polynomials and the Grunsky matrix, Constr. Approx. 47(2018) 211-235. arXiv:1606.00553
  12. B. Beckermann, A. Townsend: On the singular values of matrices with displacement structure, SIAM J. Matrix Anal. Applics. 38 (2017) 1227-1248. arxiv:1609.09494 This paper has won the SIAM Award to appear in the June 2019 SIGEST section of SIAM Review, see the above revised version ``Bounds on the Singular Values of Matrices with Displacement Structure''.

  13. B. Beckermann, Th. Helart, On the sharpness of the weighted Bernstein-Walsh inequality, with applications to the superlinear convergence of conjugate gradients (2017), arXiv:1707.07871 

  14. B. Beckermann, A.C. Matos: Algebraic properties of robust Padé approximants, J. Approx. Theory 190 (2015) 91-114 arXiv.1310.2438
  15. B. Beckermann, M. Crouzeix: Faber polynomials of matrices for non-convex sets, Jaen J. Approx. 6 (2014) 219-231. arXiv.1310.1356
  16. B. Beckermann, J. Bustamante, R. Martinez-Cruz & Jose M. Quesada : Gaussian, Lobatto and Radau positive quadrature rules with a prescribed abscissa, Calcolo 51 (2014) 319-328

  17. R. Ragonnet, R. Jumentier, B. Beckermann: Bilan du Travail d’Etude et de Recherche ”La marche de l’empereur” à l’Université de Lille 1, MATAPLI 102 (2013) 71-82. Voir aussi ici

  18. B. Beckermann, D. Kressner, Ch. Tobler: An error analysis of Galerkin projection methods for linear systems with tensor product structure, SIAM J. Num. Anal. 51 (2013) 3307-3326.
  19. C. Badea, B. Beckermann : Spectral sets. Chapter in the Handbook for Linear Algebra, editors L. Hogben et al. (2013), pp. 37.1-37.25. https://arXiv:1302.0546
  20. 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. arXiv.1105.3088
  21. B. Beckermann, D. Bessis, L. Perotti, D. Vrinceanu: Computing high precision Matrix Padé approximants, Numerical Algorithms 61 (2012) 189-208.
  22. B. Beckermann : An error analysis for rational Galerkin projection applied to the Sylvester equation, SIAM J. Num. Anal. 49 (2012), 2430-2450.
  23. B. Beckermann, S. Guettel: Superlinear convergence of the rational Arnoldi method for the approximation of matrix functions, Numer. Mathematik 121 (2012), 205-236.
  24. B. Beckermann, V. Kalyagine, A.C. Matos, F. Wielonsky: How well does the Hermite-Pad´e approximation smooth the Gibbs phenomenon ? Math. Comp. 80 (2011), 931-958.
  25. B. Beckermann, M. Derevyagin, A. Zhedanov, The linear pencil approach to rational interpolation, J. Approx. Theory 162 (2010) 1322-1346. arXiv.0908.3381
  26. B.Beckermann, S. Güttel, R. Vandebril, On the convergence of rational Ritz values, SIAM J. Matrix Anal. Applics. 31 (2010) 1740–1774.
  27. 23. B. Beckermann, L. Reichel, Error estimation and evaluation of matrix functions via the Faber transform, SIAM J. Num. Anal. 47 (2009) 3849-3883. 
  28. B. Beckermann, A. Gryson, Extremal rational functions on symmetric discrete sets and superlinear convergence of the ADI method, Constr. Approx. 32 (2010) 393-428.

  29. B. Beckermann, G. Labahn, Fraction-Free Computation of Simultaneous Pad´e Approximants, Proceedings of ISSAC’09 Seoul, ACM Press (2009) 15-22.

  30. C. Badea, B. Beckermann, M. Crouzeix, Intersections of several disks of the Riemann sphere as Kspectral sets, Commun. Pure Appl. Anal. 8(2009) 37–54. arXiv.0908.3381
  31. H. Joulak, B. Beckermann, On Gautschi’s conjecture for generalized Gauss-Radau and Gauss-Lobatto formulae, J. Comput. Appl. Math. 233 (2009) 768-774. arXiv:0803.2281
  32. B. Beckermann, L. Reichel, The Arnoldi process and GMRES for nearly symmetric matrices, SIAM J. Matrix Anal. Appl. 30 (2008) 102-120.
  33. B. Beckermann, A.C. Matos, F. Wielonsky, Reduction of the Gibbs phenomenon for smooth functions with jumps by the ϵ-algorithm, J. Comput. Appl. Math. 219 (2008) 329-349.
  34. C. Badea, B. Beckermann, M. Crouzeix : K-spectral sets and intersections of disks of the Riemann sphere, Universit´e de Lille (2007). arxiv:0712.0522
  35. B. Beckermann, M. Crouzeix, Operators with numerical range in a conic domain, Archiv der Mathematik 88 (2007) 547-559.
  36. B. Beckermann, S. Serra Capizzano, On the asymptotic spectrum of Finite Element matrix sequences, SIAM J. Numer. Anal. 45 (2007) 746-769.
  37. B. Beckermann, G. Golub, G. Labahn, On the numerical condition of a generalized Hankel eigenvalue problem, Numer. Mathematik 106 (2007) 41-68.

  38. M. Lapik, B. Beckermann: The interval of equilibrium for the constrained energy problem in the presence of an external field, Université de Lille (2006).

  39. 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.
  40. B. Beckermann, M. Crouzeix, A lenticular version of a von Neumann inequality, Archiv der Mathematik 86 (2006) 352-355.
  41. B. Beckermann, Image numérique, GMRES et polynômes de Faber, C. R. Acad. Sci. Paris, Ser. I 340 (2005) 855-860.
  42. B. Beckermann, S.A. Goreinov, E.E. Tyrtyshnikov : Some remarks on the Elman estimate for GMRES, SIAM J. Matrix Anal. Appl. 27 (2006) 772-778.
  43. B. Beckermann, H. Cheng, G. Labahn : Fraction-free Row Reduction of Matrices of Ore Polynomials, J. Symbolic Computation 41 (2006) 513-543.
  44. B. Beckermann, J. Coussement, W. Van Assche : Multiple Wilson and Jacobi-Pineiro polynomials, J. Approx. Theory 132 (2005) 155-181. arXiv:0303093
  45. B. Beckermann, A. Martinez, E. Rakhmanov, F. Wielonsky : Asymptotic upper bounds for the entropy of orthogonal polynomials in the Szeg˝o class, J. Math. Physics 45 (2004) 4239-4254. arXiv:0311055
  46. C. Roland, B. Beckermann, C. Brezinski : Altman’s methods revisited, Applicationes Mathematicæ 31 (2004) 353-368.
  47. B. Beckermann, M. Castro, On the determinacy of complex Jacobi matrices, Math. Scand. 95 (2004), 285-298.
  48. B. Beckermann, A. Osipov, Some spectral properties of infinite band matrices, Numerical Algorithms 34 (2003) 173-185.
  49. B. Beckermann, G. Labahn, G. Villard : Normal Forms for General Polynomial Matrices, J. Symbolic Computation 41(2006) 708-737.
  50. B. Beckermann, A.B.J. Kuijlaars : Superlinear CG convergence for special right-hand sides, Electr. Trans. Num. Anal. 14 (2002) 1-19.
  51. 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.
  52. B. Beckermann, A.B.J. Kuijlaars : On the sharpness of an asymptotic error estimate for Conjugate Gradients, BIT 41 (2001), 856–867.
  53. 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.
  54. B. Beckermann, A.B.J. Kuijlaars : Superlinear Convergence of Conjugate Gradients, SIAM J. Num. Anal. 39 (2001) 300-329.
  55. B. Beckermann : Complex Jacobi matrices, J. Comput. Appl. Math. 127 (2001) 17-65.
  56. 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).
  57. B. Beckermann, G. Labahn : Fraction-free Computation of Matrix Rational Interpolants and Matrix GCD’s, SIAM J. Matrix Anal. Appl. 22 (2000) 114-144. abstract
  58. B. Beckermann, G. Labahn : Numeric and symbolic computation of problems defined by structured linear systems, Reliable Computing 6 (2000) 365-390.
  59. B. Beckermann : On a conjecture of E.A. Rakhmanov, Constructive Approximation 16 (2000) 427-448.
  60. B. Beckermann : The Condition Number of real Vandermonde, Krylov and positive definite Hankel matrices, Numer. Math. 85 (2000) 553-577.
  61. B. Beckermann : A note on the convergence of Ritz values for sequences of matrices, Publication ANO 408, Université de Lille (2000).
  62. 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. abstract
  63. B. Beckermann, E.B. Saff : On the sensitivity of least squares polynomial approximation, dans: Proceedings of a Confererence on Orthogonal Polynomials, Oberwolfach, W. Gautschi e.a. (eds), Int. Ser. of Num. Math. 131, Birkhäuser, Basel (1999) 1-19.
  64. B. Beckermann : On the classification of the spectrum of second order difference operators, Math. Nachr. 216 (2000), 45-59.
  65. B. Beckermann, G. Labahn, G. Villard : Shifted Normal Forms of Polynomial Matrices, Proceedings of ISSAC’99 Vancouver, ACM Press (1999) 189-196.
  66. B. Beckermann, E. Bourreau : How to choose modified moments? J. Comput. Appl. Math. 98 (1998) 81-98. abstract
  67. B. Beckermann, G. Labahn : When are two numerical polynomials relatively prime? J. Symbolic Computation 26 (1998) 677-689. abstract
  68. B. Beckermann, G. Labahn : A fast and numerically stable Euclidean-like algorithm for detecting relatively prime numerical polynomials. J. Symbolic Computation 26 (1998) 691-714.
  69. B. Beckermann, V. Kaliaguine : The diagonal of the Pad´e table and the approximation of the Weyl function of second order difference operators, Constructive Approximation 13 (1997) 481-510. abstract
  70. P.R. Graves–Moris, B. Beckermann : The Compass (Star) Identity for Vector-valued Rational Interpolants, Advances in Computational Mathematics 7 (1997) 279-294. abstract
  71. B. Beckermann, S. Cabay, G. Labahn : Fraction-free Computation of Matrix Padé Systems, Proceedings of ISSAC’97 Mauï, ACM Press (1997) 125-132. abstract
  72. B. Beckermann, G. Labahn : Recursiveness in Matrix Rational Interpolation Problems, J. Comput. Appl. Math. 77 (1997) 5-34. abstract
  73. B. Beckermann : The stable computation of formal orthogonal polynomials, Numerical Algorithms 11 (1996) 1-23. abstract
  74. B. Beckermann, C. Carstensen : QD–type algorithms for the non–normal Newton–Padé Approximation Table, Constructive Approximation 12 (1996) 307-330. abstract
  75. B. Beckermann : On the numerical condition of polynomial bases : Estimates for the Condition Number of Vandermonde, Krylov and Hankel matrices, Habilitationsschrift, Universität Hannover, April 1996. abstract
  76. B. Beckermann, J. Gilewicz, E. Leopold : Recurrence relations with periodic coefficients and Chebyshev polynomials, Applicationes Mathematicæ 23 (1995) 319-323.
  77. G. Labahn, B. Beckermann, S. Cabay : Inversion of Mosaic Hankel Matrices via Matrix Polynomials, Lin. Alg. Applics. 221 (1995) 253-279.
  78. J. Wimp, B. Beckermann : Families of Two-point Padé Approximants and New 4F3(1) Identities, SIAM J. Math. Anal. 26 (1995) 761-773.
  79. B. Beckermann : Nonsymmetric difference operators and polynomials being orthogonal with respect to rectangular matrix valued measures, Publication ANO 335, Université de Lille (1995). abstract
  80. 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. abstract
  81. J. Wimp, B. Beckermann : Some explicit formulas for Padé approximants of ratios of hypergeometric functions, WSSIAA 2 (1992) 427-434. abstract
  82. B. Beckermann, G. Mühlbach : A general determinantal identity of Sylvester’s type and some applications, Lin. Alg. Applics. 197 (1994) 93-112. abstract
  83. 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. abstract
  84. M. Van Barel, B. Beckermann, A. Bultheel, G. Labahn : Matrix rational interpolation with poles as interpolation points, Nonlinear Numerical Methods and Rational Approximation, (A. Cuyt ed.), Kluwer Academic Publishers, (1994) 137-148. abstract
  85. B. Beckermann, C. Carstensen : A reliable Modification of the Cross Rule for Rational Hermite Interpolation, Numerical Algorithms 3 (1992) 29-44. abstract
  86. 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. abstract
  87. 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. abstract
  88. B. Beckermann, J. Wimp : Some Dynamically Trivial Mappings, with Applications to the Improvement of Simple Iteration, Computers & Mathematics with applications 24 (1992) 89-97.
  89. 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.
  90. B. Beckermann, C. Carstensen : Global Identities in the Non-Normal Newton-Pad´e Approximation table, J. Approx. Theory 74(1993) 199-220. abstract
  91. B. Beckermann, A. Neuber, G. Mühlbach : Shanks’ transformation revisited, Lin. Alg. Applics. 173 (1992) 191-219. abstract
  92. B. Beckermann : A reliable method for computing M-Pad´e approximants on arbitrary staircases, J. Comput. Appl. Math. 40 (1992) 19-42. abstract
  93. B. Beckermann, C. Carstensen : On the Computation of the Non-Normal Rational Hermite-Interpolation Table, Technical Paper # 241, Univ. Hannover, 1991. abstract
  94. B. Beckermann : The Structure of the Singular Solution Table of the M-Padé Approximation Problem, J. Comput. Appl. Math. 32 (1990) 3-15.
  95. B. Beckermann : Zur Interpolation mit polynomialen Linearkombinationen beliebiger Funktionen, Dissertationsschrift, Universität Hannover, Januar 1990.
  96. 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.