Vassil Alexandrov
Hartree Centre-STFC, UK
This talk focuses on hybrid Monte Carlo methods and algorithms for Linear Algebra. It presents the Markov Chain Monte Carlo Method for Matrix Inversion (MC)2MI method, which is used as a preconditioner, and then for solving the corresponding system of linear equations, iterative methods, such as generalized minimal residuals (GMRES) or bi-conjugate gradient (stabilized) (BICGstab), are employed. Results of computational experiments with ((MC)2MI) on several accelerator architectures are presented. Their impact on performance and scalability of the method is investigated. Further 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.