Warren D. Smith

activity

19922015

most citedLinear-time nearest point algorithms for Coxeter lattices

21 citations · 61 across the 7 of their papers we have counts for

collaborators

7 papers

math.CO2015★ 4 cited

Probabilistic lower bounds on maximal determinants of binary matrices

Richard P. Brent, Judy-anne H. Osborn, Warren D. Smith

Let $D (n)$ be the maximal determinant for $n \times n$ ${\pm 1}$ -matrices, and $R (n) = D (n) / n^{n /2}$ be the ratio of $D (n)$ to the Hadam…

math.CO2014★ 1 cited

Lower bounds on maximal determinants of binary matrices via the probabilistic method

Richard P. Brent, Judy-anne H. Osborn, Warren D. Smith

Let $D (n)$ be the maximal determinant for $n \times n$ ${\pm 1}$ -matrices, and $R (n) = D (n) / n^{n /2}$ be the ratio of $D (n)$ to the Hadamard upper bound. We give severa…

math.NA2014★ 21 cited

Bounds on determinants of perturbed diagonal matrices

Richard P. Brent, Judy-anne H. Osborn, Warren D. Smith

We give upper and lower bounds on the determinant of a perturbation of the identity matrix or, more generally, a perturbation of a nonsingular diagonal matrix. The matrices conside…

math.CO2012★ 9 cited

Lower bounds on maximal determinants of +-1 matrices via the probabilistic method

Richard P. Brent, Judy-anne H. Osborn, Warren D. Smith

We show that the maximal determinant D(n) for $n \times n$ $\pm 1$ -matrices satisfies $R (n) := D (n) / n^{n /2} \geq κ_{d} > 0$ . Here $n^{n /2}$ is the Hadamard upper bound, and $κ_{d}$ de…

cs.IT2009★ 21 cited

Linear-time nearest point algorithms for Coxeter lattices

Robby G. McKilliam, Warren D. Smith, I. Vaughan L. Clarkson

The Coxeter lattices, which we denote $A_{n / m}$ , are a family of lattices containing many of the important lattices in low dimensions. This includes $A_{n}$ , $E_{7}$ , $E_{8}$ and their d…

math.CO2003★ 4 cited

New lower bounds for the maximal determinant problem

William P. Orrick, Bruce Solomon, Roland Dowdeswell +1

We report new world records for the maximal determinant of an n-by-n matrix with entries +/-1. Using various techniques, we beat existing records for n=22, 23, 27, 29, 31, 33, 34,…