@Article{EAJAM-7-21,
author = {Cun-Qiang Miao},
title = {A Filtered-Davidson Method for Large Symmetric Eigenvalue Problems},
journal = {East Asian Journal on Applied Mathematics},
year = {2018},
volume = {7},
number = {1},
pages = {21--37},
abstract = {<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>},
issn = {2079-7370},
doi = {https://doi.org/10.4208/eajam.160816.131016a},
url = {http://global-sci.org/intro/article_detail/eajam/10732.html}
}