On Advanced Monte Carlo Methods for Linear Algebra on Advanced Accelerator Architectures
<|reference_start|>On Advanced Monte Carlo Methods for Linear Algebra on Advanced Accelerator Architectures: In this paper we present computational experiments with the Markov Chain Monte Carlo Matrix Inversion ($(\text{MC})^2\text{MI}$) on several accelerator architectures and investigate their impact on performance and scalability of the method. The method is used as a preconditioner and for solving the corresponding system of linear equations iterative methods, such as generalized minimal residuals (GMRES) or bi-conjugate gradient (stabilized) (BICGstab), are used.   Numerical experiments are carried out to highlight the benefits and deficiencies of both approaches and to assess their overall usefulness in light of scalability of the method.<|reference_end|>
@article{lebedev2024on,
    title={On Advanced Monte Carlo Methods for Linear Algebra on Advanced
  Accelerator Architectures},
    author={Anton Lebedev and Vassil Alexandrov},
    journal={2018 IEEE/ACM 9th Workshop on Latest Advances in Scalable
  Algorithms for Large-Scale Systems (scalA), Dallas, TX, USA, 2018, pp. 81-90},
    year={2024},
    doi={10.1109/ScalA.2018.00014},
    archivePrefix={arXiv},
    eprint={2409.03095},
    primaryClass={math.NA cs.DC cs.NA}
}