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Power Method

The power method, described in Algorithm 4.1, can be used to solve the NHEP without any apparent change.

\begin{algorithm}{The Power Method for the
Computation of $\lambda_{\max}(A)$} ...
(4) \> \> \> Else $z := y /\Vert y\Vert _2$.
Under conditions similar to those in the Hermitian case, the power method for the non-Hermitian matrix $A$ converges to $\lambda_{\max}(A)$, the largest eigenvalue in magnitude. The convergence rate depends on the ratio $\vert \lambda_2 / \lambda_{\max}\vert$, where $\lambda_2$ is the second largest eigenvalue of $A$ in magnitude. For detailed discussions of the power method, see Wilkinson [457], Golub and Van Loan [198], and Demmel [114].

Susan Blackford 2000-11-20