TY - JOUR
T1 - Extrapolating the Arnoldi Algorithm to Improve Eigenvector Convergence
AU - Pollock , Sara
AU - Scott , L.Ridgway
JO - International Journal of Numerical Analysis and Modeling
VL - 5
SP - 712
EP - 721
PY - 2021
DA - 2021/08
SN - 18
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/ijnam/19389.html
KW - Eigenvalue computation, extrapolation, Arnoldi algorithm
AB - <p style="text-align: justify;">We consider extrapolation of the Arnoldi algorithm to accelerate computation of
the dominant eigenvalue/eigenvector pair. The basic algorithm uses sequences of Krylov vectors
to form a small eigenproblem which is solved exactly. The two dominant eigenvectors output
from consecutive Arnoldi steps are then recombined to form an extrapolated iterate, and this
accelerated iterate is used to restart the next Arnoldi process. We present numerical results
testing the algorithm on a variety of cases and find on most examples it substantially improves
the performance of restarted Arnoldi. The extrapolation is a simple post-processing step which
has minimal computational cost.</p>