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Rayleigh Quotient Iteration.

Similar to inverse iteration, the Rayleigh quotient iteration (RQI) method of §4.3 can also be generalized to solve the problem (5.1).


\begin{algorithm}{RQI for GHEP} { \begin{tabbing} (nr)ss\=ijkl\=bbb\=ccc\=ddd\= ... ...bda=\rho_{k}$\ for most recent $k$\ and $x=v$ \end{tabbing}} \par\end{algorithm}

The only difference between Algorithms 5.2 and 5.3 is in step (8), where the shift is updated. This makes it necessary to perform a sparse factorization in step (3) in each iteration. The reward for this is a cubic rate of convergence.


Susan Blackford 2000-11-20