An Arnoldi--Schur Algorithm for Large Eigenproblems

Sorensen's iteratively restarted Arnoldi algorithm is one of the mostsuccessful and flexible methods for finding a few eigenpairs of a
large matrix. However, the need to preserve structure of the Arnoldi
decomposition, on which the algorithm is based, restricts the range of
transformations that can be performed on it. In consequence, it is
difficult to deflate converged Ritz vectors from the decomposition.
Moreover, the potential forward instability of the implicit QR
algorithm can cause unwanted Ritz vectors to persist in the
computation. In this paper we introduce a generalized Arnoldi
decomposition that solves both problems in a natural and efficient
manner.
(Also cross-referenced as UMIACS-TR-2000-21)