Now showing items 1-16 of 16

• #### Complex symmetric stabilizing solution of the matrix equation $X+A^{T}X^{-1}A=Q$ ﻿

(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 ...
• #### 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 ...
• #### Convergence rates of some iterative methods for nonsymmetric algebraic Riccati equations arising in transport theory ﻿

(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.
• #### A convergence result for matrix Riccati differential equations associated with M-matrices ﻿

(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 ...
• #### 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)