Computations of Eigenpair Subsets with the MRRR Algorithm
The main advantage of inverse iteration over the QR algorithm and Divide & Conquer for the symmetric tridiagonal eigenproblem is that subsets of eigenpairs can be computed at reduced cost. The MRRR algorithm (MRRR = Multiple Relatively Robust Representations) is a clever variant of inverse iteration without the need for reorthogonalization. STEGR, the current version of MRRR in LAPACK 3.0, does not allow for subset computations. The next release of STEGR is designed to compute a (sub-)set of k eigenpairs with {Omicron}(kn) operations. Because of the special way in which eigenvectors are computed, MRRR subset computations are more complicated than when using inverse iteration. Unlike the latter, MRRR sometimes cannot ignore the unwanted part of the spectrum. We describe the problems with what we call 'false singletons'. These are eigenvalues that appear to be isolated with respect to the wanted eigenvalues but in fact belong to a tight cluster of unwanted eigenvalues. This paper analyzes these complications and ways to deal with them.
- Research Organization:
- Ernest Orlando Lawrence Berkeley NationalLaboratory, Berkeley, CA (US)
- Sponsoring Organization:
- USDOE Director, Office of Science; National ScienceFoundation
- DOE Contract Number:
- AC02-05CH11231
- OSTI ID:
- 922844
- Report Number(s):
- LBNL--60374; BnR: YN0100000
- Journal Information:
- Numerical Linear Algebra with Applications, Journal Name: Numerical Linear Algebra with Applications Journal Issue: 8 Vol. 13
- Country of Publication:
- United States
- Language:
- English
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