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EB13 Sparse unsymmetric: Arnoldi’s method

Given a real unsymmetric $n\times n$ 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.