## Search

Now showing items 11-16 of 16

#### 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, ...

#### 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 $R$ ...

#### On Newton's method and Halley's method for the principal $p$th root of a matrix

(Elsevier, 2010)

If $A$ is a matrix with no negative real eigenvalues
and all zero eigenvalues of $A$ are semisimple, the principal
$p$th root of $A$ can be computed by Newton's method or Halley's method,
with a preprocessing procedure ...

#### 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.