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#### 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 ...

#### Faculty of Science annual report, January 1, 2007 - December 31, 2007

(Faculty of Science, University of Regina, 2007)

#### Faculty of Science annual report, January 1, 2006 - December 31, 2006

(Faculty of Science, University of Regina, 2006)

#### Department of Mathematics and Statistics Annual Report 2004

(Department of Mathematics and Statistics, University of Regina, 2004)

#### Faculty of Science annual report, January 1, 2005 - December 31, 2005

(Faculty of Science, University of Regina, 2005)

#### Faculty of Science annual report, January 1, 2004 - December 31, 2004

(Faculty of Science, University of Regina, 2004)

#### Creating our future: 2005-2010 : a strategic plan for the Faculty of Science

(Faculty of Science, University of Regina, 2004-09)

#### 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 ...

#### 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)

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 + ...