On a shrink-and-expand technique for block eigensolvers
<|reference_start|>On a shrink-and-expand technique for block eigensolvers: In block eigenvalue algorithms, such as the subspace iteration algorithm and the locally optimal block preconditioned conjugate gradient (LOBPCG) algorithm, a large block size is often employed to achieve robustness and rapid convergence. However, using a large block size also increases the computational cost. Traditionally, the block size is typically reduced after convergence of some eigenpairs, known as deflation. In this work, we propose a non-deflation-based, more aggressive technique, where the block size is adjusted dynamically during the algorithm. This technique can be applied to a wide range of block eigensolvers, reducing computational cost without compromising convergence speed. We present three adaptive strategies for adjusting the block size, and apply them to four well-known eigensolvers as examples. Theoretical analysis and numerical experiments are provided to illustrate the efficiency of the proposed technique. In practice, an overall acceleration of 20% to 30% is observed.<|reference_end|>
@article{liu2024on,
    title={On a shrink-and-expand technique for block eigensolvers},
    author={Yuqi Liu and Yuxin Ma and Meiyue Shao},
    journal={arXiv preprint arXiv:2409.05572},
    year={2024},
    archivePrefix={arXiv},
    eprint={2409.05572},
    primaryClass={math.NA cs.NA}
}