Publications Bernhard Beckermann

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Published papers - Submitted papers - Other publications
Published in Mathematical Journals (refereed):
  1. B. Beckermann, A.B.J. Kuijlaars : On the sharpness of an asymptotic error estimate for Conjugate Gradients, Publication ANO 412, Université de Lille (2000). To appear in BIT (2002).

  2. (Click here for an abstract | Get Postscript manuscript | Get pdf manuscript )
  3. B. Beckermann, M. Castro Smirnova, V. Kaliaguine: A recurrence relation connected to the convergence of vector S-fractions, Publication ANO 431, Université de Lille (2001). To appear in East Journal on Approximations. (2002).

  4. (Click here for an abstract | Get Postscript manuscript | Get pdf manuscript )
  5. B. Beckermann, A.B.J. Kuijlaars : Superlinear CG convergence for special right-hand sides, Publication ANO 415, Université de Lille (2000). To appear in Electr. Trans. Numer. Anal. (2001).

  6. (Click here for an abstract | Get Postscript manuscript | Get pdf manuscript )
  7. B. Beckermann, A.B.J. Kuijlaars: Superlinear Convergence of Conjugate Gradients, SIAM J. Num. Anal. 39 (2001) 300-329.

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

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

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

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

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

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

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

  22. (Click here for an abstract | Get Postscript manuscript | Get pdf manuscript )
  23. 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.

  24. (Click here for an abstract | Get Postscript manuscript | Get pdf manuscript )
  25. 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.

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

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

  30. (Click here for an abstract)
  31. 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.

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

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

  36. (Click here for an abstract)
  37. 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.

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

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

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

  44. (Click here for an abstract)
  45. B. Beckermann, J. Gilewicz, E. Leopold: Recurrence relations with periodic coefficients and Chebyshev polynomials, Applicationes Mathematicae 23 (1995) 319-323.
  46. G. Labahn, B. Beckermann, S. Cabay: Inversion of Mosaic Hankel Matrices via Matrix Polynomials, Lin. Alg. Applics. 221 (1995) 253-279.
  47. J. Wimp, B. Beckermann, Families of Two-point Padé Approximants and New $4F3$ Identities, SIAM J. Math. Anal. 26 (1995) 761-773.
  48. 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.

  49. (Click here for an abstract)
  50. 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.

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

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

  55. (Click here for an abstract)
  56. 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.

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

  59. (Click here for an abstract)
  60. 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.

  61. (Click here for an abstract)
  62. B. Beckermann, J. Wimp: Some Dynamically Trivial Mappings, with Applications to the Improvement of Simple Iteration, Computers & Mathematics with applications 24 (1992) 89-97.
  63. 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.
  64. B. Beckermann, C. Carstensen: Global Identities in the Non-Normal Newton-Padé Approximation table, J. Approx. Theory 74(1993) 199-220.

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

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

  69. (Click here for an abstract)
  70. B. Beckermann: The Structure of the Singular Solution Table of the M-Pade Approximation Problem, J. Comput. Appl. Math. 32 (1990),3-15.
  71. 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: A note on the convergence of Ritz values for sequences of matrices, Publication ANO 408, Université de Lille (2000).

  2. (Click here for an abstract | Get Postscript manuscript | Get pdf manuscript | See numerical results )
  3. 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).

  4. (Click here for an abstract | Get Postscript manuscript | Get pdf manuscript )

Other publications:

  1. B. Beckermann: Zur Interpolation mit polynomialen Linearkombinationen beliebiger Funktionen, Dissertationsschrift, Universität Hannover, Januar 1990.
  2. B. Beckermann, C. Carstensen: On the Computation of the Non-Normal Rational Hermite-Interpolation Table, Grüne Reihe # 241, Univ. Hannover, 1991.

  3. (Click here for an abstract)
  4. 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).

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

  7. (Click here for an abstract)
  8. B. Beckermann: On the numerical condition of polynomial bases: Estimates for the Condition Number of Vandermonde, Krylov and Hankel matrices, Habilitationsschrift, Universität Hannover (1996).

  9. (Click here for an abstract)

Last changes: Aug 20, 01
bbecker@ano.univ-lille1.fr