## Search

Now showing items 31-40 of 76

#### 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 ...

#### 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. ...

#### 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 + ...

#### 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, ...