## Search

Now showing items 1-10 of 16

#### 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 ...

#### Solving a structured quadratic eigenvalue problem by a structure-preserving doubling algorithm

(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 ...

#### Monotone convergence of Newton-like methods for M-matrix algebraic Riccati equations

(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 ...

#### 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 ...

#### 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 ...

#### 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 ...

#### 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 ...

#### Performance enhancement of doubling algorithms for a class of complex nonsymmetric algebraic Riccati equations

(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 ...

#### On algebraic Riccati equations associated with M-matrices

(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 ...

#### 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 ...