Publications
Refereed Journal Papers
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B. Beckermann, G. Golub and G. Labahn,
On the numerical condition of a generalized Hankel eigenvalue problem,
Numerische Mathematik, (2007), 106(1) (2007) 41-68.
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H. Cheng and G. Labahn,
Output-sensitive Modular Algorithms for Polynomial Matrix Normal Forms,
To appear in Journal of Symbolic Computation 25 pages.
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B. Beckermann, G. Labahn and G. Villard,
Normal Forms for General Polynomial
Matrices, Journal of Symbolic Computation, 41(6) (2006) 708-737.
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B. Beckermann, H. Cheng and G. Labahn,
Fraction-free Row Reduction of Matrices of Ore Polynomials,
Journal of Symbolic Computation 41(5) (2006) 513-543.
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Y. d'Halluin, P.A. Forsyth and G. Labahn,
A Semi-Lagrangian approach for
American Asian Options under jump diffusion,
SIAM Journal of Scientific Computation 27 (2005) 315-345.
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Y. d'Halluin, P.A. Forsyth, G. Labahn,
A Penalty Method for American Options with Jump Diffusion Processes.
Numerische Mathematik, 97:2 (2004) 321-352.
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Y. d'Halluin, P.A. Forsyth, K.R. Vetzal, G. Labahn,
A Numerical PDE Approach for Pricing Callable Bonds.
Applied Mathematical Finance 8 (2001) 49-77.
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B. Beckermann and G. Labahn,
Fraction-free Computation of Matrix Rational Interpolants and Matrix GCD's.
SIAM J. Matrix Analysis and Applications.
22(1) (2000) 114-144.
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B. Beckermann and G. Labahn,
Effective Computation of Rational
Approximants and Interpolants.
Reliable Computing 6 (2000) 365-390.
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B. Beckermann and G. Labahn,
When are two numerical polynomials relatively prime?
Journal of Symbolic Computation 26 (1998) 677-689.
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B. Beckermann and G. Labahn,
A fast and numerically stable Euclidean--like
algorithm for detecting relatively prime numerical polynomials.
Journal of Symbolic Computation 26 (1998) 691-714.
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A. Storjohann and G. Labahn,
A Fast Las Vegas Algorithm for
Computing the Smith Normal Form of a Polynomial Matrix,
Linear Algebra and its Applications. 253 (1997) 155-173.
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B. Beckermann and G. Labahn,
Recursiveness in Matrix Rational Interpolation Problems,
J. of Computational and Applied Math 77 (1997) 5-34.
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S. Cabay, A.R. Jones and G. Labahn,
Experiments with a Weakly Stable Algorithm
for Computing Pad\'e-Hermite and Simultaneous Pad\'e Approximants,
ACM Trans. of Mathematical Software (TOMS) 23(1) (1997) 91-110.
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S. Cabay, A.R. Jones and G. Labahn,
Computation of Numerical
Pade-Hermite and Simultaneous Pade Systems I: Near Inversion of
Generalized Sylvester Matrices,
SIAM J. Matrix Analysis and Applications 17 (1996) 247-267.
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S. Cabay, A.R. Jones and G. Labahn,
Computation of Numerical
Pade-Hermite and Simultaneous Pade Systems II: A Weakly-Stable
Algorithm,
SIAM J. Matrix Analysis and Applications, 17, (1996), 268-297.
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G. Labahn, B. Beckermann and S. Cabay,
Inversion of Mosaic Hankel Matrices via Matrix Polynomial Systems,
Linear Algebra and its
Applications 221 (1995), 253-280.
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B. Beckermann and G. Labahn,
A uniform approach for the fast computation of Matrix-type Pade approximants,
SIAM J. Matrix Analysis and Applications (1994), 804-823.
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G. Labahn and T. Shalom,
Inversion of Toeplitz Structured Matrices using only Standard Equations,
Linear Algebra and its Applications
207 (1994), 49-70.
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G. Labahn,
Inversion Components for Block Hankel-like Matrices,
Linear Algebra and its Applications, 177 (1992), pp. 7-48.
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B. Beckermann and G. Labahn,
A uniform approach for Hermite Pade
and simultaneous Pade Approximants and their Matrix-type
generalizations,
Numerical Algorithms, 3 (1992), pp. 45-54.
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G. Labahn and T. Shalom,
Inversion of Toeplitz Matrices with only Two Standard Equations,
Linear Algebra and its Applications, 175 (1992), pp. 143-158.
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S. Cabay and G. Labahn,
A Superfast Algorithm for Multi-dimensional Pade Approximation,
Numerical Algorithms, 2 (1992), pp. 201-224.
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S. Cabay, G. Labahn and B. Beckermann,
On the Theory and Computation of Non-perfect Pade-Hermite
Approximants,
Journal of Applied and Computational Math, 39 (1992), pp. 295-313.
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G. Labahn, D.K. Choi and S. Cabay,
Inverses of Block Hankel and
Block Toeplitz Matrices,
SIAM J. of Computing, 19 (1990), pp. 98-123.
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T.C. Scott, R.A. Moore, G.J. Fee, M.B. Monagan, G. Labahn and
K.O. Geddes, Perturbative Solutions of Quantum Mechanical Problems
by Symbolic Computation: A Review, International J. of Modern Phys.
C, 1 (1990), pp. 53-76.
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G. Labahn and S. Cabay,
Matrix Pade Fractions and their Computation,
SIAM J. of Computing, 18 (1989), pp. 639-657.
Refereed Conference Papers
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H. Cheng and G. Labahn,
On Computing Polynomial GCD in Alternate Bases,
Proceedings of ISSAC'06, Genoa, Italy, ACM Press, (2006) 47-54.
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M. Giesbrecht, G. Labahn and W-s Lee,
Symbolic-numeric Sparse Interpolation of Multivariate Polynomials,
Proceedings of ISSAC'06, Genoa, Italy, ACM Press, (2006) 116-123.
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M. Giesbrecht, G. Labahn and Y. Zhang,
Computing Valuation Popov Forms,
Proceedings of CASA'2005,
Lecture Notes on Computer Science 3516, Springer-Verlag, (2005) 619-626.
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G. Labahn and Ziming Li,
Hyperexponential Solutions of Finite-rank
Ideals in Orthogonal Ore Algebras,
Proceedings of ISSAC'04, Santander,
Spain, ACM Press, (2004) 213-220.
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R. Burger, G. Labahn and M. van Hoeij,
Closed form solutions of linear odes
having elliptic functions as coefficients, Proceedings of ISSAC'04,
Santander, Spain, ACM Press, (2004) 58-64.
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M. Giesbrecht, G. Labahn and W-s Lee,
Symbolic-Numeric Sparse Polynomial
Interpolation in Chebyshev Basis and Trigonometric Interpolation,
Proceedings
of Computer Algebra in Scientific Computing (CASC 2004), St. Petersburg,
Russia, (2004)
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C.P. Jeannerod and G. Labahn,
The SNAP Package for Arithmetic with Numeric Polynomials,
Proceedings of International Congress of Mathematical Software 2002,
Beijing, China, (2002) 61-71.
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B. Beckermann, H. Cheng and G. Labahn,
Fraction-free Row Reduction of Matrices of Skew Polynomials,
Proceedings of ISSAC'02, Lille, France, ACM Press, (2002) 8-15.
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H. Cheng and G. Labahn,
Computing all Factorizations in Z_N[x],
Proceedings of ISSAC'01, London, Canada, ACM Press, (2001) 64-71.
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B. Beckermann, G. Labahn and G. Villard,
Shifted Normal Forms of Polynomial Matrices.
Proceedings of ISSAC'99, Vancouver, ACM Press, (1999) 189-196.
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B. Beckermann, S. Cabay and G. Labahn,
Fraction-free Computation of Matrix Pade Systems,
Proceedings of ISSAC'97, Maui, ACM Press, (1997) 125-132.
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D.J. Jeffrey, G. Labahn, M. von Mohrenschildt and A.D. Rich,
Integration of the signum, piecewise and related functions,
Proceedings of ISSAC'97, Maui, ACM Press, (1997) 324-330.
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W. Heidrich, R. Bartels and G. Labahn,
Fitting Uncertain Data with NURBS,
Proceedings of Curves and Surfaces, Chamonix, France, (1997)
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A. Storjohann and G. Labahn,
Asymptotically Fast Computation of
Hermite Normal Forms of Integer Matrices
Proceedings of ISSAC 96, ACM Press, (1996), pp. 259-266.
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K.O. Geddes and G. Labahn,
Symbolic and Numeric Integration in Maple,
Proceedings of the First Asian Technology Conference in Mathematics,
(1995), pp. 377-386.
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K.O. Geddes and G. Labahn,
The Maple Computer Algebra System,
Proceedings of the First Asian Technology Conference in Mathematics,
(1995), pp. 367-376.
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A. Storjohann and G. Labahn,
Preconditioning of Rectangular
Polynomial Matrices for Efficient Hermite Normal Form computation,
Proceedings of ISSAC 95, ACM Press, (1995), pp. 119-125.
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M. Van Barel, B. Beckermann, A. Bultheel and G. Labahn,
Matrix Rational Interpolation with Pole Information,
Nonlinear Numerical Methods and Rational Approximation,
(A. Cuyts ed.), Kluwer Academic
Publishers, (1994), pp 137-148.
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S. Cabay and G. Labahn,
A Fast, Reliable Algorithm for Calculating Pade-Hermite Forms,
Proceedings of ISSAC 89, (G.H. Gonnet ed.), ACM
Press, (1989), pp. 95-100.
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G. Labahn and S. Cabay, Matrix Pade Fractions, Proceedings of
EUROCAL 87, (J. Davenport ed.), Lecture Notes in Computer Science,
Springer-Verlag, (1989), pp. 438-449.
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S. Cabay and G. Labahn,
Fast, Numerically Stable Inversion of Mosaic Hankel Matrices,
Systems and Networks: Mathematical Theory
and Applications, Volume II: Invited and Contributed Papers, (U.
Helmke, R. Mennicken and J. Saurer, ed.) Akademie Verlag (1994), 625-630.
Books
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K.O. Geddes, S.R. Czapor and G. Labahn, ``Algorithms for Computer
Algebra'', Kluwer Academic Publishers, (1992), 585 pages.
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M.B. Monagan, K.O. Geddes, K.M. Heal, G. Labahn, S. Vorketter, J. McCarron,
P DeMarco, ``The Maple Introductory Programming Guide'', Springer-Verlag,
(2003), 370 pages.
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M.B. Monagan, K.O. Geddes, K.M. Heal, G. Labahn, S. Vorketter, J. McCarron,
P DeMarco, ``The Maple Advanced Programming Guide'', Springer-Verlag,
(2003), 430 pages.
Others
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G. Labahn, S. Maclean, M. Marzouk, I. Rutherford and D. Tausky,
A preliminary report on the MathBrush pen-math system,
Proc. of Maple Conference 2006, (2006) 162-178.
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G. Labahn and T. Humphries,
Symbolic Interation of Jacobian Elliptic Functions in Maple,
Proc. of Maple Conference 2005, (2005) 331-339.
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M. Giesbrecht, G. Labahn and W-s Lee,
Symbolic-Numeric Sparse Polynomial Interpolation of Multivariate Polynomials,
Proc. 9th Rhine Workshop on Computer Algebra (2004).
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G. Labahn,
Solving Linear Differential Equations in Maple,
MapleTech, 2 (1995), 20-28.
Miscellaneous
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G. Labahn
Kamke's Second Order Linear ODEs in Maple,
(2000)
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G. Labahn
Kamke's Third Order Linear ODEs in Maple,
(2000)
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G. Labahn
Kamke's Fourth Order Linear ODEs in Maple,
(2000)
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G. Labahn
Kamke's Fifth and Higher Order Linear ODEs in Maple,
(2000)
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