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Now showing items 1-4 of 4

#### 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 ...

#### 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, ...

#### 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.