## Search

Now showing items 1-10 of 16

#### 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 ...

#### 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 ...

#### Numerical solution of nonlinear matrix equations arising from Green's function calculations in nano research

(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 $R$ ...

#### 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 ...

#### 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 ...

#### 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 ...