Parallel Approaches in the Heavy Ball GMRES Method

Linear system is a useful mathematical model that is used in many research areas. This paper presents a parallelism study that considers a recent iterative method to solve large sparse linear systems, called Heavy Ball Generalized Minimal Residual (HBGMRES) method. This method is based on the classical restarted GMRES and tries to add some history in each iteration. Our parallelism study is made with the OpenMP API, based on the shared memory paradigm. We proposed three different parallel approaches. Our experimental results show a maximum speedup of 2.11 on a four-core processor.