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  1. The generalized minimum residual method (GMRES) is a commonly used iterative Krylov solver for sparse, non-symmetric systems of linear equations. Like other iterative solvers, data movement dominates its run time. To improve this performance, we propose running GMRES in reduced precision with key operations remaining in full precision. Additionally, we provide theoretical results linking the convergence of finite precision GMRES with classical Gram-Schmidt with reorthogonalization (CGSR) and its infinite precision counterpart which helps justify the convergence of this method to double-precision accuracy. We tested the mixed-precision approach with a variety of matrices and preconditioners on a GPU-accelerated node. Excluding themore »incomplete LU factorization without fill in (ILU(0)) preconditioner, we achieved average speedups ranging from 8 to 61 percent relative to comparable double-precision implementations, with the simpler preconditioners achieving the higher speedups.« less
  2. In this paper, we present work towards the development of a new data analytics and machine learning (ML) framework, called MagmaDNN. Our main goal is to provide scalable, high-performance data analytics and ML solutions for scientific applications running on current and upcoming heterogeneous many-core GPU-accelerated architectures. To this end, since many of the functionalities needed are based on standard linear algebra (LA) routines, we designed MagmaDNN to derive its performance power from the MAGMA library. The close integration provides the fundamental (scalable high-performance) LA routines available in MAGMA as a backend to MagmaDNN. We present some design issues for performancemore »and scalability that are specific to ML using Deep Neural Networks (DNN), as well as the MagmaDNN designs towards overcoming them. In particular, MagmaDNN uses well established HPC techniques from the area of dense LA, including task-based parallelization, DAG representations, scheduling, mixed-precision algorithms, asynchronous solvers, and autotuned hyperparameter optimization. We illustrate these techniques and their incorporation and use to outperform other frameworks, currently available.« less