Optimal Polynomial Smoothers for Parallel AMG
<|reference_start|>Optimal Polynomial Smoothers for Parallel AMG: In this paper, we propose some Chebyshev polynomials of the 1st-kind which produce optimal bound for a polynomial dependent constant involved in the AMG $V$-cycle error bound and do not require information about the spectrum of matrices. We formulate a variant of a minimax problem already proposed in [J. Lottes, Optimal polynomial smoothers for multigrid V-cycles, Numer. Lin. Alg. with Appl., 30 (2023), p. e2518, https://doi.org/10.1002/nla.2518] and define Chebyshev polynomial of the 1st-kind as acceleration for a weighted-Jacobi smoother; we also describe efficient GPU kernels for the application of the polynomial smoother and compare results with accelerators defined in [J. Lottes, Optimal polynomial smoothers for multigrid V-cycles, Numer. Lin. Alg. with Appl., 30 (2023), p. e2518, https://doi.org/10.1002/nla.2518] on usual benchmarks at very large scales.<|reference_end|>
@article{d'ambra2024optimal,
    title={Optimal Polynomial Smoothers for Parallel AMG},
    author={Pasqua D'Ambra, Fabio Durastante, Salvatore Filippone, Stefano Massei,
  Stephen Thomas},
    journal={arXiv preprint arXiv:2407.09848},
    year={2024},
    archivePrefix={arXiv},
    eprint={2407.09848},
    primaryClass={math.NA cs.NA}
}