2020-07-30 –, Green Track
This work presents a parallel implementation of Monte Carlo-Markov Chain method for solving systems of linear algebraic equations using Julia and GPU accelerator. Julia 1.1.0 + CUDAnative.jl provide several advantages regarding development and performance which help to delve into convergence and precision analysis. This work is supported by PAPIIT-IA104720.
During the last 5 years we have been working on the iterative methods for solving systems of linear algebraic equations. Recently our work has focused on estimates inverse matrix of the system and an efficient condicioner in order to obtain a good approximate solution. We use for this task Markov Chain-Monte Carlo (MCMC) method as a theoretical basis. Iterative process, convergence, random sampling and calculation of weights and estimators represent an exhaustive computational effort for the MCMC method as the size of the system of linear equations to be solved increases. In order to tackle this problem paralllel implementation using Julia 1.1.0 + CUDAnative is proposed.
Julia programming language has captured our attention since it has consolidated, as an excellent development environment for scientific computation. Our contribution to the Julia conference 2020 is to show parallel implementation of the MCMC method highlighting the advantages of CUDAnative.jl as a wrapper of GPU accelerators. Convergence and scaling results are discused at the end of the talk.
We would like to thank the financial support of PAPIIT-IA104720.
Oscar A. Esquivel-Flores received his Bachelor's degree in Applied Mathematics and Computing from Universidad Nacional Autónoma de México (UNAM). M.S. degree in Computer Sciences from Universidad Autónoma Metropolitana, México and PhD degree in Computer Engineering from UNAM in 2013. He has working on parallel and high performance computing as part of a posdoctoral position at the Barcelona Supercomputing Center as an international agreement with National Council of Science and Technology of México. He currently helds a research position in Instituto de Investigaciones en Matemáticas Aplicadas y en Sistemas at Universidad Nacional Autónoma de México developing parallel algorithms regard matrix computations, machine learning and optimization.
Degree in physics. Currently studying data science and interested in AI, high-performance computing, and computational physics.
Studying at the National Autonomous University of Mexico.