## Version 1.1.1

4th April 2013

Recent Changes

• Single
• Double

### EB13 Sparse unsymmetric: Arnoldi’s method

Given a real unsymmetric $n×n$ matrix $A=\left\{{a}_{ij}\right\}$, this routine uses Arnoldi based methods to calculate the $r$ eigenvalues ${\lambda }_{i},i=1,...,r$, that are of largest absolute value, or are right-most, or are of largest imaginary parts. The right-most eigenvalues are those with the most positive real part. There is an option to compute the associated eigenvectors ${y}_{i}$, $i=1,...,r$, where ${Ay}_{i}={\lambda }_{i}{y}_{i}$. The routine may be used to compute the left-most eigenvalues of $A$ by using $-A$ in place of $A$.

The Arnoldi methods oﬀered by EB13 are:

(1) The basic (iterative) Arnoldi method.
(2) Arnoldi’s method with Chebyshev acceleration of the starting vectors.
(3) Arnoldi’s method applied to the preconditioned matrix ${p}_{l}\left(A\right)$, where ${p}_{l}$ is a Chebyshev polynomial.

Each method is available in blocked and unblocked form.