Publications (23)
Fast and deterministic computation of the determinant of a polynomial matrix
Wei Zhou, George Labahn
Given a square, nonsingular matrix of univariate polynomials over a field , we give a deterministic algorithm for finding the d…
A cubic algorithm for computing the Hermite normal form of a nonsingular integer matrix
Stavros Birmpilis, George Labahn, Arne Storjohann
A Las Vegas randomized algorithm is given to compute the Hermite normal form of a nonsingular integer matrix of dimension . The algorithm uses quadratic integer multiplicati…
Existence Problem of Telescopers: Beyond the Bivariate Case
Shaoshi Chen, Qing-Hu Hou, George Labahn +1
In this paper, we solve the existence problem of telescopers for rational functions in three discrete variables. We reduce the problem to that of deciding the summability of bivari…
Computing critical points for invariant algebraic systems
Jean-Charles Faugère, George Labahn, Mohab Safey El Din +2
Let be a field and , in be multivariate polynomials (with ) invariant under the action of $\…
Convergence of implicit schemes for Hamilton-Jacobi-Bellman quasi-variational inequalities
Parsiad Azimzadeh, Erhan Bayraktar, George Labahn
In [Azimzadeh, P., and P. A. Forsyth. "Weakly chained matrices, policy iteration, and impulse control." SIAM J. Num. Anal. 54.3 (2016): 1341-1364], we outlined the theory and imple…
Faster real root decision algorithm for symmetric polynomials
George Labahn, Cordian Riener, Mohab Safey El Din +2
In this paper, we consider the problem of deciding the existence of real solutions to a system of polynomial equations having real coefficients, and which are invariant under the a…
Constructing minimal telescopers for rational functions in three discrete variables
Shaoshi Chen, Qing-Hu Hou, Hui Huang +2
We present a new algorithm for constructing minimal telescopers for rational functions in three discrete variables. This is the first discrete reduction-based algorithm that goes b…
Bohemian Matrix Geometry
Robert M. Corless, George Labahn, Dan Piponi +1
A Bohemian matrix family is a set of matrices all of whose entries are drawn from a fixed, usually discrete and hence bounded, subset of a field of characteristic zero. Originally…
-Monotone Fourier Methods for Optimal Stochastic Control in Finance
Peter A. Forsyth, George Labahn
Stochastic control problems in finance often involve complex controls at discrete times. As a result numerically solving such problems, for example using methods based on partial d…
Computing Nearby Non-trivial Smith Forms
Mark Giesbrecht, Joseph Haraldson, George Labahn
We consider the problem of computing the nearest matrix polynomial with a non-trivial Smith Normal Form. We show that computing the Smith form of a matrix polynomial is amenable to…
A C implementation of the Smith massager algorithm
Ziwen Wang, Stavros Birmpilis, George Labahn +1
We describe a C implementation of the Las Vegas algorithm of Birmpilis, Labahn and Storjohann from 2020 for computing the Smith normal form of a nonsingular integer matrix. The alg…
Rank-Sensitive Computation of the Rank Profile of a Polynomial Matrix
George Labahn, Vincent Neiger, Thi Xuan Vu +1
Consider a matrix of univariate polynomials over a field . We study the problem of computing the column rank profile of $\ma…
Efficient Rational Creative Telescoping
Mark Giesbrecht, Hui Huang, George Labahn +1
We present a new algorithm to compute minimal telescopers for rational functions in two discrete variables. As with recent reduction-based approaches, our algorithm has the importa…
Computing Lower Rank Approximations of Matrix Polynomials
Mark Giesbrecht, Joseph Haraldson, George Labahn
Given an input matrix polynomial whose coefficients are floating point numbers, we consider the problem of finding the nearest matrix polynomial which has rank at most a specified…
Fast, deterministic computation of the Hermite normal form and determinant of a polynomial matrix
George Labahn, Vincent Neiger, Wei Zhou
Given a nonsingular matrix of univariate polynomials over a field , we give fast and deterministic algorithms to compute its determinant and its Hermite no…
Homotopy techniques for solving sparse column support determinantal polynomial systems
George Labahn, Mohab Safey El Din, Ãric Schost +1
Let be a field of characteristic zero with its algebraic closure. Given a sequence of polynomials $\mathbf{g} = (g_1, \ldots, g_s) \in \mathbf{…
Numerical methods for optimal decumulation of a defined contribution pension plan
Peter A. Forsyth, George Labahn
The decumulation of a defined contribution (DC) pension plan is well known to be one of the hardest problems in finance. We model this decumulation challenge as an optimal stochast…
A fast, deterministic algorithm for computing a Hermite Normal Form of a polynomial matrix
George Labahn, Wei Zhou
Given a square, nonsingular matrix of univariate polynomials over a field , we give a fast, deterministic algorithm for find…
Computing bases in Hermite normal form of lattices of integer relations
George Labahn, Arne Storjohann
Given a full column rank and an we present an algorithm to compute the basis in Hermite form of the integer lattice…
On rational functions without Froissart doublets
Bernhard Beckermann, George Labahn, Ana C. Matos
In this paper we consider the problem of working with rational functions in a numeric environment. A particular problem when modeling with such functions is the existence of Froiss…
Efficient q-Integer Linear Decomposition of Multivariate Polynomials
Mark Giesbrecht, Hui Huang, George Labahn +1
We present two new algorithms for the computation of the q-integer linear decomposition of a multivariate polynomial. Such a decomposition is essential for the treatment of q-hyper…
A Bayesian model for recognizing handwritten mathematical expressions
Scott MacLean, George Labahn
Recognizing handwritten mathematics is a challenging classification problem, requiring simultaneous identification of all the symbols comprising an input as well as the complex two…
A fast algorithm for computing the Smith normal form with multipliers for a nonsingular integer matrix
Stavros Birmpilis, George Labahn, Arne Storjohann
A Las Vegas randomized algorithm is given to compute the Smith multipliers for a nonsingular integer matrix , that is, unimodular matrices and such that , with $S…