## Search

Now showing items 1-10 of 12

#### 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 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 ...

#### 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 ...

#### On a nonlinear matrix equation arising in nano research

(SIAM, 2012)

The matrix equation $X+A^{T}X^{-1}A=Q$ arises in Green's function calculations in nano
research, where $A$ is a real square matrix and $Q$ is a real symmetric matrix dependent on a parameter
and is usually indefinite. ...

#### The matrix equation $X+A^TX^{-1}A=Q$ and its application in nano research

(SIAM, 2010)

The matrix equation $X+A^TX^{-1}A=Q$ has been studied extensively when $A$
and $Q$ are real square matrices
and $Q$ is symmetric positive definite. The equation has positive definite
solutions under suitable conditions, ...

#### 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 $R$ ...