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Mathematics > Numerical Analysis

arXiv:2409.03095 (math)
[Submitted on 4 Sep 2024]

Title:On Advanced Monte Carlo Methods for Linear Algebra on Advanced Accelerator Architectures

Authors:Anton Lebedev, Vassil Alexandrov
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Abstract: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.
Comments: 10 pages, 8 figures, 2 pages IEEE artifact information, accepted to the 9th Workshop on Latest Advances in Scalable Algorithms for Large-Scale Systems
Subjects: Numerical Analysis (math.NA); Distributed, Parallel, and Cluster Computing (cs.DC)
ACM classes: G.1.3; G.3
Cite as: arXiv:2409.03095 [math.NA]
  (or arXiv:2409.03095v1 [math.NA] for this version)
  https://doi.org/10.48550/arXiv.2409.03095
Journal reference: 2018 IEEE/ACM 9th Workshop on Latest Advances in Scalable Algorithms for Large-Scale Systems (scalA), Dallas, TX, USA, 2018, pp. 81-90
Related DOI: https://doi.org/10.1109/ScalA.2018.00014

Submission history

From: Anton Lebedev [view email]
[v1] Wed, 4 Sep 2024 21:48:49 UTC (630 KB)
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