TY - JOUR
T1 - A Filtered-Davidson Method for Large Symmetric Eigenvalue Problems
AU - Cun-Qiang Miao
JO - East Asian Journal on Applied Mathematics
VL - 1
SP - 21
EP - 37
PY - 2018
DA - 2018/02
SN - 7
DO - http://doi.org/10.4208/eajam.160816.131016a
UR - https://global-sci.org/intro/article_detail/eajam/10732.html
KW - Symmetric eigenproblem, filtering technique, Chebyshev polynomials, Krylov subspace, Davidson-type method.
AB - <p style="text-align: justify;">For symmetric eigenvalue problems, we constructed a three-term recurrence
polynomial filter by means of Chebyshev polynomials. The new filtering technique does
not need to solve linear systems and only needs matrix-vector products. It is a memory
conserving filtering technique for its three-term recurrence relation. As an application,
we use this filtering strategy to the Davidson method and propose the filtered-Davidson
method. Through choosing suitable shifts, this method can gain cubic convergence rate
locally. Theory and numerical experiments show the efficiency of the new filtering technique.</p>