# Faculty of Science: Recent submissions

• (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 ...
• (Public Knowledge Network, 2013)
We establish the bounds 4 on the Nordhaus- Gaddum sum upper bound multipliers for all graphs G, in connections with certain Colin de Verdi ere type graph parameters. The Nordhaus-Gaddum sum lower bound is conjectured ...
• (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 ...
• (PLOS ONE, 2014-05-15)
Fire Blight is a destructive disease of apple and pear caused by the enteric bacterial pathogen, Erwinia amylovora. E. amylovora initiates infection by colonizing the stigmata of apple and pear trees, and entering the ...
• (Elsevier, 2008)
The fixed-point iteration is a simple method for finding the maximal Hermitian positive definite solutions of the matrix equations $X\pm A^*X^{-1}A=I$ (the plus/minus equations). The convergence of this method ...
• (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 ...
• (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 ...
• (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 $f(x) = x^*(A + iB)x/|x^*(A + ... • (Elsevier, 2010) If$A$is a matrix with no negative real eigenvalues and all zero eigenvalues of$A$are semisimple, the principal$p$th root of$A$can be computed by Newton's method or Halley's method, with a preprocessing procedure ... • (Elsevier, 2010) We determine and compare the convergence rates of various fixed-point iterations for finding the minimal positive solution of a class of nonsymmetric algebraic Riccati equations arising in transport theory. • (SIAM, 2010) The matrix equation$X+A^TX^{-1}A=Q$has been studied extensively when$A$and$Q$are real square matrices and$Q$is symmetric positive definite. The equation has positive definite solutions under suitable conditions, ... • (SIAM, 2010) In studying the vibration of fast trains, we encounter a palindromic quadratic eigenvalue problem (QEP)$(\lambda^2 A^T + \lambda Q + A)z = 0$, where$A, Q \in \mathbb{C}^{n \times n}$and$Q^T = Q$. Moreover, the matrix ... • (Elsevier, 2011) We study the matrix equation$X+A^{T}X^{-1}A=Q$, where$A$is a complex square matrix and$Q$is complex symmetric. Special cases of this equation appear in Green's function calculation in nano research and also in the ... • (SIAM, 2012) The matrix equation$X+A^{T}X^{-1}A=Q$arises in Green's function calculations in nano research, where$A$is a real square matrix and$Q$is a real symmetric matrix dependent on a parameter and is usually indefinite. ... • (Elsevier, 2012) The Green's function approach for treating quantum transport in nano devices requires the solution of nonlinear matrix equations of the form$X+(C^*+{\rm i} \eta D^*)X^{-1}(C+{\rm i} \eta D)=R+{\rm i}\eta P$, where$R$... • (Taylor & Francis, 2013) We start with a discussion of coupled algebraic Riccati equations arising in the study of linear-quadratic optimal control problem for Markov jump linear systems. Under suitable assumptions, this system of equations has ... • (Springer, 2013) For the algebraic Riccati equation whose four coefficient matrices form a nonsingular$M$-matrix or an irreducible singular$M$-matrix$K$, the minimal nonnegative solution can be found by Newton's method and the doubling ... • (Elsevier, 2013) We consider the algebraic Riccati equation for which the four coefficient matrices form an$M$-matrix$K$. When$K$is a nonsingular$M$-matrix or an irreducible singular$M$-matrix, the Riccati equation is known to have ... • (Oxford University Press, 2014) A new class of complex nonsymmetric algebraic Riccati equations has been studied by Liu and Xue (SIAM J. Matrix Anal. Appl., 33 (2012), 569-596), which is related to the M-matrix algebraic Riccati equations. Doubling ... • (2014-04-22) The initial value problem for a matrix Riccati differential equation associated with an$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 ...