Using small eigenproblems to accelerate power method iterations

Sara Pollock; L. Ridgway Scott. 5 July, 2021.
Communicated by L. Ridgway Scott.


We consider algorithms that operate on sequences of Krylov vectors generated by the (inverse) power method that accelerate computation of the dominant eigenvalue. The algorithms use subsequent Krylov vectors to form a small eigenproblem which is solved exactly. The dominant eigenvector is used to restart the Krylov process. We explain this in detail using just two subsequent vectors, and then we generalize the algorithm to use multiple Krylov vectors. We show how this is related to restarted Arnoldi and other methods.

Original Document

The original document is available in PDF (uploaded 5 July, 2021 by L. Ridgway Scott).