Publications Bernhard Beckermann
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Published papers -
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Other publications
Published in Mathematical Journals (refereed):
- 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).
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- 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).
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- 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).
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- B. Beckermann, A.B.J. Kuijlaars:
Superlinear Convergence of Conjugate Gradients,
SIAM J. Num. Anal. 39 (2001) 300-329.
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- B. Beckermann: Complex Jacobi matrices,
J. Comput. Appl. Math. 127 (2001) 17-65.
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- B. Beckermann, G. Labahn: Numeric and symbolic computation
of problems defined by structured linear systems,
Reliable Computing 6 (2000) 365-390.
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- B. Beckermann: The Condition Number of real Vandermonde,
Krylov and positive definite Hankel matrices,
Numer. Mathematik 85 (2000) 553-577.
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- B. Beckermann, G. Labahn: Fraction-free Computation
of Matrix Rational Interpolants and Matrix GCD's,
SIAM J. Matrix Anal. Appl. 22 (2000) 114-144.
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- B. Beckermann: On a conjecture of E.A. Rakhmanov,
Constructive Approximation 16 (2000) 427-448.
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- B. Beckermann: On the classification of the spectrum
of second order difference operators, Mathematische
Nachrichten 216 (2000), 45-59.
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- B. Beckermann, G. Labahn, G. Villard: Shifted Normal
Forms of Polynomial Matrices, Proceedings of ISSAC'99 Vancouver, ACM
Press (1999) 189-196.
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- 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.
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- 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.
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- B. Beckermann, E. Bourreau: How to choose modified
moments? J. Comput. Appl. Math. 98 (1998) 81-98.
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- B. Beckermann, G. Labahn: When are two numerical polynomials
relatively prime? J. Symbolic Computations 26 (1998) 677-689.
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- 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.
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- B. Beckermann, S. Cabay, G. Labahn: Fraction-free Computation
of Matrix Padé Systems, Proceedings of ISSAC'97 Maui, ACM
Press (1997) 125-132.
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- P.R. Graves--Morris, B. Beckermann: The Compass (Star)
Identity for Vector-valued Rational Interpolants, Advances in Computational
Mathematics 7 (1997) 279-294.
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- 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.
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- B. Beckermann, G. Labahn: Recursiveness in Matrix Rational
Interpolation Problems, J. Comput. Appl. Math. 77 (1997) 5-34.
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- B. Beckermann: The stable computation of formal orthogonal
polynomials, Numerical Algorithms 11 (1996) 1-23.
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- B. Beckermann, C. Carstensen: QD--type algorithms for
the non--normal Newton--Padé Approximation Table, Constructive
Approximation 12 (1996) 307-330.
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- B. Beckermann, J. Gilewicz, E. Leopold: Recurrence
relations with periodic coefficients and Chebyshev polynomials, Applicationes
Mathematicae 23 (1995) 319-323.
- G. Labahn, B. Beckermann, S. Cabay: Inversion of Mosaic
Hankel Matrices via Matrix Polynomials, Lin. Alg. Applics. 221
(1995) 253-279.
- J. Wimp, B. Beckermann, Families of Two-point Padé
Approximants and New $4F3$ Identities, SIAM J. Math. Anal. 26
(1995) 761-773.
- 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.
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- 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.
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- J. Wimp, B. Beckermann, Some explicit formulas for
Pade approximants of ratios of hypergeometric functions, WSSIAA
2 (1992) 427-434.
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- B. Beckermann, G. Mühlbach: A general determinantal
identity of Sylvester's type and some applications, Lin. Alg. Applics.
197 (1994) 93-112.
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- 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.
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- B. Beckermann, C. Carstensen: A reliable Modification
of the Cross Rule for Rational Hermite Interpolation, Numerical Algorithms
3 (1992) 29-44.
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- 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.
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- B. Beckermann, J. Wimp: Some Dynamically Trivial Mappings,
with Applications to the Improvement of Simple Iteration, Computers
& Mathematics with applications 24 (1992) 89-97.
- 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.
- B. Beckermann, C. Carstensen: Global Identities in the
Non-Normal Newton-Padé Approximation table, J. Approx. Theory
74(1993) 199-220.
(Click here for an abstract)
- B. Beckermann, A. Neuber, G. Mühlbach: Shanks'
transformation revisited, Lin. Alg. Applics. 173 (1992) 191-219.
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- B. Beckermann: A reliable method for computing M-Padé
approximants on arbitrary staircases, J. Comput. Appl. Math. 40
(1992) 19-42.
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- B. Beckermann: The Structure of the Singular Solution
Table of the M-Pade Approximation Problem, J. Comput. Appl. Math.
32 (1990),3-15.
- 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:
- B. Beckermann:
A note on the convergence of Ritz values for sequences of matrices,
Publication ANO 408, Université de Lille (2000).
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- 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).
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Other publications:
- B. Beckermann: Zur Interpolation mit polynomialen Linearkombinationen
beliebiger Funktionen, Dissertationsschrift, Universität Hannover,
Januar 1990.
- B. Beckermann, C. Carstensen: On the Computation of
the Non-Normal Rational Hermite-Interpolation Table, Grüne Reihe #
241, Univ. Hannover, 1991.
(Click here for an abstract)
- 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).
(Click here for an abstract)
- B. Beckermann: Nonsymmetric difference operators and
polynomials being orthogonal with respect to rectangular matrix valued
measures, Publication ANO 335, Université de Lille (1995).
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- B. Beckermann: On the numerical condition of polynomial
bases: Estimates for the Condition Number of Vandermonde, Krylov and
Hankel matrices, Habilitationsschrift, Universität Hannover (1996).
(Click here for an abstract)
Last changes: Aug 20, 01
bbecker@ano.univ-lille1.fr