George Labahn
I am interested in many areas of computational mathematics. My main area
of research lies in the field of Computer Algebra with a secondary area
being in the field of Computational Finance. In addition, I am the
principal researcher in the MathBrush project, which seeks to create software
for doing mathematics on penbased devices.
My work on computer algebra centers on effective algorithms for both exact
and symbolicnumeric computation. My work includes algorithms for
Matrix Normal Forms (polynomial and Ore domains), Greatest Common Divisors of
numeric polynomials, Differential equations (particularly those with elliptic
functions as coefficients) and Rational Approximation and Interpolation. My
main coauthor in this topic (and numerous other topics) is
Bernhard Beckermann
My work in computational finance centers on fast, stable methods for
solving financial option problems, particularly options whose underlying
asset follows a jump diffusion pricing model. My main coauthor in this
topic is
Peter Forsyth
My work on penbased mathematics centers on the development of the
MathBrush penmath system. This work includes recognition of handwritten
mathematics along with understanding how mathematics can be done using
only a pen and a computer algebra backend,.
I am an associate editor of
Journal of Symbolic Computation (JSC).
I am a former associate editor of
ACM Transactions of Mathematical Software (TOMS).
My CV
Publications list
Talks
Computer Algebra
 Order/Sigma bases
[ Ref1,
Ref2,
Ref3]
(with B. Beckermann)
Fast algorithms for Order Bases
[ Ref1 Ref2](with W. Zhou)
 Fast algorithms for polynomial matrix arithmetic
[ Ref1,
Ref2,
Ref3,
Ref4]
(with W. Zhou)

Fractionfree algorithms for computing matrix GCD's and matrix rational
interpolants [ Ref1, Ref2, Ref3]
(with B. Beckermann)
Fractionfree algorithms for computing normal forms of
polynomial matrices (with B. Beckermann and G. Villard
[Ref1, Ref2])
and Ore polynomials (with B. Beckermann and H. Cheng
[Ref3]).
 Scaling and finite abelian group symmetries
[Ref1,Ref2 , Ref3 ]
(with E. Hubert)
 Probabilistic algorithms for Hermite and Smith normal forms of
polynomial matrices
[Ref1, Ref2,
Ref3]
(with A. Storjohann)
 Seminumerical Computations: GCD's of numerical polynomials
[Ref1, Ref2]
(with B. Beckermann).
The SNAP package (with CP Jeannerod)
[Ref]
Rational functions (with B. Beckermann and A. Matos)
[Ref]

Seminumerical sparse interpolation of black box polynomials
[Ref1,
Ref2] (
with M. Giesbrecht and Ws Lee)
and the numerical conditioning of these
and related problems [Ref2]
(with B. Beckermann and G. Golub).
 Closed form solutions of linear odes having elliptic functions as coefficients (with R. Burger and M. van Hoeij)
[Ref].
Hyperexponential solutions of
orthogonal systems of Ore operators (with Ziming Li)
[Ref]
Differential equations in Maple (old)
[Ref]
Computational Finance
 Pricing of convertable bonds (with Y. d'Halluin, P.A. Forsyth and
K. Vetzal [Ref])
 Penalty method for American options with jump diffusion
(with Y. d'Halluin and P.A. Forsyth
[Ref])
 Asian options with american conditions under jump diffusion processes
(with Y. d'Halluin and P.A. Forsyth
[Ref])
 Controlled HJB PDEs in Finance
(with P.A. Forsyth
[Ref])
 Guaranteed Benefit contracts
(with A. Belanger and P.A. Forsyth
[Ref])
 Singular Control Problems in Finance
(with P.A. Forsyth and I. Huang
[Ref1,
Ref2,
Ref3,
Ref4])
Rational Approximation
 Uniform computation of matrix rational approximants (with B. Beckermann)
[Ref1,
Ref2,
Ref3,
Ref4, Ref5]
 Fast, numerically stable computation of matrix Pade approximants
(with S. Cabay and T. Jones)
[Ref1,
Ref2,
Ref3]
Structured Matrices
Inversion of structured matrices (with B. Beckermann, D.K. Choi, S. Cabay, T. Shalom)
[Ref1,
Ref2,
Ref3,
Ref4,
Ref5]
Pen Math Interfaces
 The MathBrush pen math system
[ Ref1,
Ref2, Ref3 ]
 Recognizers for handwritten math
[ Ref1 ,
Ref2 ]
(with S. Maclean)
 Matrix algebra and pen math input
[ Ref ]
 PenMath corpora [Ref]
Integration of Elliptic Functions (2004)
Solving linear ODEs with doubly periodic coefficients (2003,2004)
The Matrix Polynomial Algebra package in Maple (2002)
The SNAP package in Maple (with C.P. Jennerod) (2001)
Special function solutions of higher order linear odes using the Meijer G function (2000)
Solving linear differential equation using differential factorization (19992000)
Solution of linear differential equations via special functions in Maple (19962000)
The DEtools package for working with differential equations in Maple (19921998)
Computation of indefinite Elliptic integrals in Maple (1996)
The Plots graphics package in Maple (19901995)
The Plottools graphics package in Maple (1995)
The inttrans package for computation of integral transforms in Maple (19921995)
Computation of definite Elliptic Integrals in Maple (19911996)
The linear ODE solver in Maple (19931998)
The Mpade package for matrix rational approximation (in Maple share library) (1993)
Matrix similarity in Maple (1994)
Frobenius and Jordan Normal Forms in Maple (19921995)
Indefinite Integration of Bessel Functions in Maple (1993)
Extensions of Risch Algorithm for functions defined by integrals in Maple (1992)
Implementation of bivariate modular gcd algorithm in Maple (1991)
Computation of the Matrix Exponential in Maple (1989)
Other Pictures
Miscellaneous: York Tournament
Last modified May 2018, 2018