TY - JOUR
T1 - Implicitly Restarted Refined Generalised Arnoldi Method with Deflation for the Polynomial Eigenvalue Problem
JO - East Asian Journal on Applied Mathematics
VL - 1
SP - 82
EP - 99
PY - 2018
DA - 2018/02
SN - 8
DO - http://doi.org/10.4208/eajam.070517.180917a
UR - https://global-sci.org/intro/article_detail/eajam/10886.html
KW - Polynomial eigenvalue problem, generalised Arnoldi method, refinement, implicit restarting, non-equivalence low-rank deflation.
AB - <p style="text-align: justify;">Based on the generalised Arnoldi procedure, we develop an implicitly restarted
generalised Arnoldi method for solving the large-scale polynomial eigenvalue problem.
By combining implicit restarting with the refinement scheme, we present an implicitly
restarted refined generalised Arnoldi (IRGAR) method. To avoid repeated converged
eigenpairs in the later iteration, we develop a novel non-equivalence low-rank deflation
technique and propose a deflated and implicitly restarted refined generalised Arnoldi
method (DIRGAR). Some numerical experiments show that this DIRGAR method is efficient
and robust.</p>