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 pen-based devices.
My work on computer algebra centers on effective algorithms for both exact
and symbolic-numeric 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 co-author 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 co-author in this
topic is
Peter Forsyth
My work on pen-based 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
Computer Algebra
-
Fraction-free algorithms for computing matrix GCD's and matrix rational
interpolants [ Ref1, Ref2, Ref3]
(with B. Beckermann)
Fast algorithms for Order Bases
[ Ref](with W. Zhou)
Fraction-free 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]).
- Probabilistic algorithms for Hermite and Smith normal forms of
polynomial matrices (with A. Storjohann)
[Ref1, Ref2,
Ref3]
- Semi-numerical Computations: GCD's of numerical polynomials
[Ref1, Ref2]
(with B. Beckermann).
The SNAP package (with C-P Jeannerod)
[Ref]
-
Semi-numerical sparse interpolation of black box polynomials
[Ref1,
Ref2] (
with M. Giesbrecht and W-s 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])
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 ]
- Matrix algebra and pen math input
[ Ref ]
- PenMath corpora [Ref]
