# Browsing Mathematics & Statistics Faculty by Title

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• C.V. ﻿
(2014-01-21)
• (International Linear Algebra Society, 2013-01)
The Colin de Verdi`ere parameters mu and nu are defined to be the maximum nullity of certain real symmetric matrices associated with a given graph. In this work, both of these parameters are calculated for all chordal ...
• (Elsevier, 2011)
We study the matrix equation $X+A^{T}X^{-1}A=Q$, where $A$ is a complex square matrix and $Q$ is complex symmetric. Special cases of this equation appear in Green's function calculation in nano research and also in the ...
• (SIAM, 2009)
In this paper, we review two types of doubling algorithm and some techniques for analyzing them. We then use the techniques to study the doubling algorithm for three different nonlinear matrix equations in the critical ...
• (Elsevier, 2010)
We determine and compare the convergence rates of various fixed-point iterations for finding the minimal positive solution of a class of nonsymmetric algebraic Riccati equations arising in transport theory.
• (2014-04-22)
The initial value problem for a matrix Riccati differential equation associated with an $M$-matrix is known to have a global solution $X(t)$ on $[0, \infty)$ when $X(0)$ takes values from a suitable set of nonnegative ...
• (SIAM, 2009)
Hyperbolic quadratic matrix polynomials $Q(\lambda) = \lambda^2 A + \lambda B + C$ are an important class of Hermitian matrix polynomials with real eigenvalues, among which the overdamped quadratics are those with ...
• (Elsevier, 2015)
The enhanced principal rank characteristic sequence (epr-sequence) of a symmetric n ×n matrix is a sequence from A,S, or N according as all, some, or none of its principal minors of order k are nonzero. Such sequences give ...
• (Elsevier, 2015-08-15)
The enhanced principal rank characteristic sequence (epr-sequence) was originally defined for an n ×n real symmetric matrix or an n ×n Hermitian matrix. Such a sequence is defined to be l1l2···ln where lk is A,S, or N ...
• (SIAM Journal on Discrete Mathematics, 2014)
Let G = PGL(2, q) be the projective general linear group acting on the projec- tive line P_q. A subset S of G is intersecting if for any pair of permutations \pi and \sigma in S, there is a projective point p in P_q such ...
• (European Journal of Combinatorics, 2016)
We prove an analogue of the classical Erdős-Ko-Rado theorem for intersecting sets of permutations in finite $2$-transitive groups. Given a finite group $G$ acting faithfully and $2$-transitively on the set ...
• (SIAM J. Discrete Math. 28, 2014)
In this paper we prove an Erdős-Ko-Rado-type theorem for intersecting sets of permutations. We show that an intersecting set of maximal size in the projective general linear group $PGL_3(q)$, in its natural ...
• (SIAM, 2009)
A 25-year old and somewhat neglected algorithm of Crawford and Moon attempts to determine whether a given Hermitian matrix pair $(A,B)$ is definite by exploring the range of the function $f(x) = x^*(A + iB)x/|x^*(A + ... • (2014-01-21) • (Taylor & Francis, 2013) We start with a discussion of coupled algebraic Riccati equations arising in the study of linear-quadratic optimal control problem for Markov jump linear systems. Under suitable assumptions, this system of equations has ... • (SIAM, 2010) The matrix equation$X+A^TX^{-1}A=Q$has been studied extensively when$A$and$Q$are real square matrices and$Q$is symmetric positive definite. The equation has positive definite solutions under suitable conditions, ... • (International Linear Algebra Society, 2014-06) Barrett et al. asked in [W. Barrett et al. Minimum rank of edge subdivisions of graphs. Electronic Journal of Linear Algebra, 18:530–563, 2009.], whether the maximum nullity is equal to the zero forcing number for all ... • (2016-06) In this paper we give a proof of the Mikl´os-Manickam-Singhi (MMS) conjecture for some partial geometries. Specifically, we give a condition on partial geometries which implies that the MMS conjecture holds. Further, ... • (International Linear Algebra Society, 2013-09) The minimum number of distinct eigenvalues, taken over all real symmetric matrices compatible with a given graph G, is denoted by q(G). Using other parameters related to G, bounds for q(G) are proven and then applied to ... • (Springer, 2013) For the algebraic Riccati equation whose four coefficient matrices form a nonsingular$M$-matrix or an irreducible singular$M$-matrix$K\$, the minimal nonnegative solution can be found by Newton's method and the doubling ...