PENN STATE BEHREND
1 PRISCHAK BUILDING
ERIE PA 16563
Biography
Thomas R. Cameron is an assistant professor of Mathematics at Penn State Behrend. He is a passionate mathematics teacher and scholar whose interests lie at the intersection of algebraic graph theory, data science, and numerical analysis. In particular, his work has made notable contributions to the area of matrix polynomials, the numerical solution of polynomial equations, the characterization of digraphs, and the rankability of data.
Research Interests
Numerical linear algebra: study of matrix polynomials, the non-linear eigenvalue problem, and the numerical solution of polynomial roots; Algebraic graph theory: study of graphs using the algebraic properties of their associated matrices; Rankability of data: study of data and its inherent characteristics that make it more or less suitable for ranking
Publications
On the Laplacian spread of digraphs, Linear Algebra and its Applications - May, 2023
Collaborators: Wayne Barrett; Emily Evans; H. Tracy Hall; Mark Kempton
Constructions of cospectral graphs with different zero forcing parameters, Electronic Journal of Linear Algebra - May 5, 2022
Collaborators: Aida Abiad; Boris Brimkov; Jane Breen; Himanshu Gupta; Ralihe Villagran
On a compensated Ehrlich-Aberth method for the accurate computation of all polynomial roots, Electronic Transactions of Numerical Analysis - March 21, 2022
Collaborator: Stef Graillat
On digraphs with polygonal restricted numerical range, Linear Algebra and its Applications - March 1, 2022
Collaborators: Tracy Hall; Ben Small; Alex Wiedemann
On the Linear Ordering Problem and the Rankability of Data, Foundations of Data Science - June, 2021
Collaborators: Sebastian Charmot; Jonad Pulaj, Co-Author
On the restricted numerical range of the Laplacian matrix for digraphs, Linear and Multilinear Algebra - April 9, 2020
Collaborators: Michael Robertson; A. Wiedemann, Co-Author
On the graph Laplacian and the rankability of data, Linear Algebra and its Applications - March 1, 2020
Collaborators: A. N. Langville, Co-Author; H. C. Smith, Co-Author
On Householder sets for matrix polynomials, Linear Algebra and its Applications - January 15, 2020
Collaborator: P. J. Psarrakos, Co-Author
An effective implementation of a modified Laguerre method for the roots of a polynomial, Numerical Algorithms - 2019
On Descartes’ rule of signs for matrix polynomials, Operators and Matrices - 2019
Collaborator: P. J. Psarrakos, Co-Author
Finite precision in an infinite world, Math Horizons - August 30, 2019
Collaborator: T. P. Chartier, Co-Author
The determinant from signed volume to the Laplace expansion, American Mathematical Monthly - May 10, 2019
On the reduction of matrix polynomials to Hessenberg form, Electronic Journal of Linear Algebra - February 5, 2016
Spectral bounds for matrix polynomials with unitary coefficients, Electronic Journal of Linear Algebra - February 8, 2015
Education
Ph D, Mathematics, Washington State University
MS, Mathematics, Washington State University
BS, Mathematics, The University of Minnesota Duluth
AA, General Liberal Arts, Century College