TY - JOUR
T1 - Implicitly Restarted Refined Partially Orthogonal Projection Method with Deflation
AU - Wei Wei & Hua Dai
JO - East Asian Journal on Applied Mathematics
VL - 1
SP - 1
EP - 20
PY - 2018
DA - 2018/02
SN - 7
DO - http://doi.org/10.4208/eajam.070816.131016a
UR - https://global-sci.org/intro/article_detail/eajam/10731.html
KW - Polynomial eigenvalue problem, partially orthogonal projection method, refinement, implicitly restarting, non-equivalence low-rank deflation.
AB - <p style="text-align: justify;">In this paper we consider the computation of some eigenpairs with smallest
eigenvalues in modulus of large-scale polynomial eigenvalue problem. Recently,
a partially orthogonal projection method and its refinement scheme were presented
for solving the polynomial eigenvalue problem. The methods preserve the structures
and properties of the original polynomial eigenvalue problem. Implicitly updating the
starting vector and constructing better projection subspace, we develop an implicitly
restarted version of the partially orthogonal projection method. Combining the implicit
restarting strategy with the refinement scheme, we present an implicitly restarted refined
partially orthogonal projection method. In order to avoid the situation that the
converged eigenvalues converge repeatedly in the later iterations, we propose a novel
explicit non-equivalence low-rank deflation technique. Finally some numerical experiments
show that the implicitly restarted refined partially orthogonal projection method
with the explicit non-equivalence low-rank deflation technique is efficient and robust.</p>