@Article{JCM-37-6,
author = {Liu, Haoyang and Zaiwen, Wen and Yang, Chao and Zhang, Yin},
title = {Block Algorithms with Augmented Rayleigh-Ritz Projections for Large-Scale Eigenpair Computation},
journal = {Journal of Computational Mathematics},
year = {2019},
volume = {37},
number = {6},
pages = {889--915},
abstract = {<p style="text-align: justify;">Most iterative algorithms for eigenpair computation consist of two main steps: a subspace update (SU) step that generates bases for approximate eigenspaces, followed by
a Rayleigh-Ritz (RR) projection step that extracts approximate eigenpairs. So far the
predominant methodology for the SU step is based on Krylov subspaces that builds orthonormal bases piece by piece in a sequential manner. In this work, we investigate block
methods in the SU step that allow a higher level of concurrency than what is reachable
by Krylov subspace methods. To achieve a competitive speed, we propose an augmented
Rayleigh-Ritz (ARR) procedure. Combining this ARR procedure with a set of polynomial
accelerators, as well as utilizing a few other techniques such as continuation and deflation,
we construct a block algorithm designed to reduce the number of RR steps and elevate
concurrency in the SU steps. Extensive computational experiments are conducted in $C$ on
a representative set of test problems to evaluate the performance of two variants of our
algorithm. Numerical results, obtained on a many-core computer without explicit code
parallelization, show that when computing a relatively large number of eigenpairs, the performance of our algorithms is competitive with that of several state-of-the-art eigensolvers.</p>},
issn = {1991-7139},
doi = {https://doi.org/10.4208/jcm.1910-m2019-0034},
url = {https://global-sci.com/article/84451/block-algorithms-with-augmented-rayleigh-ritz-projections-for-large-scale-eigenpair-computation}
}