How the MRRR Algorithm Can Fail on Tight Eigenvalue Clusters
Beresford N. Parlett and Christof Vomel
In the 90s, Dhillon and Parlett devised a new algorithm (Multiple Relatively Robust Representations, MRRR) for computing numerically orthogonal eigenvectors of a symmetric tridiagonal matrix T with O(n^2) cost. It has been incorporated into LAPACK version 3.0 as routine STEGR. We have discovered that the MRRR algorithm can fail in extreme cases. Roundoff error does not always come to rescue and clusters of eigenvalues can agree to working accuracy. In this paper, we describe and analyze these failures and various remedies.
Published 2004-12-01 05:00:00 as ut-cs-04-542 (ID:203)