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.