Mo logo [home] [lexicon] [problems] [tests] [courses] [auxiliaries] [notes] [staff] german flag

Mathematics-Online lexicon: Annotation to

Von Mises-Iteration


A B C D E F G H I J K L M N O P Q R S T U V W X Y Z overview

The von Mises iteration applies powers of a matrix to a start vector $ x$. The resulting normalized sequence

$\displaystyle u_n = A^n x / \left\Vert A^n x \right\Vert _2
$

will generally approximate a dominant eigenvector. Sufficient for convergence is that $ A$ is diagonalizable and has an eigenvalue $ \lambda$ with largest absolute value. Then, for any vector $ x$ with a nontrivial component $ u$ in the eigenspace of $ \lambda$,

$\displaystyle \left\Vert e^{- \mathrm{i} n \varphi} u_n -
\frac{u }{\left\Vert...
...2} \right\Vert=
O \left( \left\vert \varrho / \lambda \right\vert^n \right)
$

with $ e^{\mathrm{i} \varphi}=\lambda / \left\vert \lambda \right\vert$ and $ \varrho$ an eigenvalue of $ A$ with second largest absolute value.

(temporary unavailable)

[Back]

  automatisch erstellt am 19.  8. 2013