Now showing items 1-20 of 33

• #### A note on the fixed-point iteration for the matrix equations $X\pm A^*X^{-1}A=I$ ﻿

(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 ...
• #### Convergence Analysis of the Doubling Algorithm for Several Nonlinear Matrix Equations in the Critical Case ﻿

(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 ...
• #### Detecting and solving hyperbolic quadratic eigenvalue problems ﻿

(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 ...
• #### An Improved Arc Algorithm for Detecting Definite Hermitian Pairs ﻿

(SIAM, 2009)
• #### Iterative methods for a linearly perturbed algebraic matrix Riccati equation arising in stochastic control ﻿

(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 ...
• #### Colin de Verdiere parameters of chordal graphs ﻿

(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 ...
• #### On the null space struture associted with trees and cycles ﻿

(The Charles Babbage Research Centre, 2013-02)
In this work, we study the structure of the null spaces of matrices associated with graphs. Our primary tool is utilizing Schur complements based on certain collections of independent vertices. This idea is applied in ...
• #### Minimum number of distinct eigenvalues of graphs ﻿

(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 ...
• #### On the relationship between zero forcing number and certain graph coverings ﻿

(2014)
The zero forcing number and the positive zero forcing number of a graph are two graph parameters that arise from two types of graph colourings. The zero forcing number is an upper bound on the minimum number of induced ...