Advanced Monte Carlo Methods for Linear Algebra on Advanced Computer Architectures
22nd May 2020, 2:00 pm – 3:00 pm
TBA, *Meeting link will be shared via email-group or contact firstname.lastname@example.org to obtain the meeting link.*
Vassil Alexandrov (Hartree Centre STFC, UK) email@example.com
Abstract—This talk will present an overview of Monte Carlo methods for Linear Algebra as well as latest advances and computational results of applying Markov Chain Monte Carlo methods for Matrix Inversion ((MC)2MI) on variety of advanced computer architectures as well as several accelerator architectures. Further, it will present experimental results for hybrid stochastic/deterministic methods, e.g. Monte Carlo/iterative ones, and in particular it will consider the case when the (MC)2MI method is used as a preconditioner for solving the corresponding system of linear equations where iterative methods, such as generalized minimal residuals (GMRES) or bi-conjugate gradient (stabilized) (BICGstab), are employed.
Numerical experiments are carried out on a selection of sparse symmetric, non-symmetric and non-structured matrices taken from the sparse matrix collection and real life problems and highlight the benefits and deficiencies of different proposed approaches to accelerate Markov Chain simulations on CPUs and accelerators alike.