Publications

Refereed Journal Papers

• 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.
  
  
• H. Cheng and G. Labahn, Output-sensitive Modular Algorithms for Polynomial Matrix Normal Forms, To appear in Journal of Symbolic Computation 25 pages.
  
  
• B. Beckermann, G. Labahn and G. Villard, Normal Forms for General Polynomial Matrices, Journal of Symbolic Computation, 41(6) (2006) 708-737.
  
  
• 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.
  
  
• 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.
  
  
• 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.
  
  
• 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.
  
  
• 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.
  
  
• B. Beckermann and G. Labahn, Effective Computation of Rational Approximants and Interpolants. Reliable Computing 6 (2000) 365-390.
  
  
• B. Beckermann and G. Labahn, When are two numerical polynomials relatively prime? Journal of Symbolic Computation 26 (1998) 677-689.
  
  
• 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.
  
  
• 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.
  
  
• B. Beckermann and G. Labahn, Recursiveness in Matrix Rational Interpolation Problems, J. of Computational and Applied Math 77 (1997) 5-34.
  
  
• 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.
  
  
• 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.
  
  
• 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.
  
  
• 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.
  
  
• 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.
  
  
• G. Labahn and T. Shalom, Inversion of Toeplitz Structured Matrices using only Standard Equations, Linear Algebra and its Applications 207 (1994), 49-70.
  
  
• G. Labahn, Inversion Components for Block Hankel-like Matrices, Linear Algebra and its Applications, 177 (1992), pp. 7-48.
  
  
• 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.
  
  
• G. Labahn and T. Shalom, Inversion of Toeplitz Matrices with only Two Standard Equations, Linear Algebra and its Applications, 175 (1992), pp. 143-158.
  
  
• S. Cabay and G. Labahn, A Superfast Algorithm for Multi-dimensional Pade Approximation, Numerical Algorithms, 2 (1992), pp. 201-224.
  
  
• 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.
  
  
• 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.
  
  
• 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.
  
  
• G. Labahn and S. Cabay, Matrix Pade Fractions and their Computation, SIAM J. of Computing, 18 (1989), pp. 639-657.
  
  

  Refereed Conference Papers

• H. Cheng and G. Labahn, On Computing Polynomial GCD in Alternate Bases, Proceedings of ISSAC'06, Genoa, Italy, ACM Press, (2006) 47-54.
  
  
• 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.
  
  
• 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.
  
  
• 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.
  
  
• 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.
  
  
• 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)
  
  
• 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.
  
  
• 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.
  
  
• H. Cheng and G. Labahn, Computing all Factorizations in Z_N[x], Proceedings of ISSAC'01, London, Canada, ACM Press, (2001) 64-71.
  
  
• B. Beckermann, G. Labahn and G. Villard, Shifted Normal Forms of Polynomial Matrices. Proceedings of ISSAC'99, Vancouver, ACM Press, (1999) 189-196.
  
  
• B. Beckermann, S. Cabay and G. Labahn, Fraction-free Computation of Matrix Pade Systems, Proceedings of ISSAC'97, Maui, ACM Press, (1997) 125-132.
  
  
• 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.
  
  
• W. Heidrich, R. Bartels and G. Labahn, Fitting Uncertain Data with NURBS, Proceedings of Curves and Surfaces, Chamonix, France, (1997)
  
  
• 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.
  
  
• 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.
  
  
• K.O. Geddes and G. Labahn, The Maple Computer Algebra System, Proceedings of the First Asian Technology Conference in Mathematics, (1995), pp. 367-376.
  
  
• 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.
  
  
• 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.
  
  
• 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.
  
  
• 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.
  
  
• 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

• K.O. Geddes, S.R. Czapor and G. Labahn, ``Algorithms for Computer Algebra'', Kluwer Academic Publishers, (1992), 585 pages.
  
  
• 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.
  
  
• 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

• 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.
  
  
• G. Labahn and T. Humphries, Symbolic Interation of Jacobian Elliptic Functions in Maple, Proc. of Maple Conference 2005, (2005) 331-339.
  
  
• M. Giesbrecht, G. Labahn and W-s Lee, Symbolic-Numeric Sparse Polynomial Interpolation of Multivariate Polynomials, Proc. 9th Rhine Workshop on Computer Algebra (2004).
  
  
• G. Labahn, Solving Linear Differential Equations in Maple, MapleTech, 2 (1995), 20-28.
  

  Miscellaneous

• G. Labahn Kamke's Second Order Linear ODEs in Maple, (2000)
  
• G. Labahn Kamke's Third Order Linear ODEs in Maple, (2000)
  
• G. Labahn Kamke's Fourth Order Linear ODEs in Maple, (2000)
  
• G. Labahn Kamke's Fifth and Higher Order Linear ODEs in Maple, (2000)