David Keyes | King Abdullah University of Science and Technology | Data-sparse Linear Algebra Algorithms for Large-scale Applications on Emerging Architectures


Friday, February 25, 2022, 1:00pm to 2:00pm



David Keyes
Director of the Extreme Computing Research Center at the King Abdullah University of Science and Technology (KAUST)

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Abstract: A traditional goal of algorithmic optimality, squeezing out flops, has been superseded by evolution in architecture. Flops no longer serve as a reasonable proxy for all aspects of complexity. Instead, algorithms must now squeeze memory, data transfers, and synchronizations, while extra flops on locally cached data represent only small costs in time and energy. Hierarchically low-rank matrices realize a rarely achieved combination of optimal storage complexity and high-computational intensity for a wide class of formally dense linear operators that arise in applications for which exascale computers are being constructed. They may be regarded as algebraic generalizations of the fast multipole method. Methods based on these hierarchical data structures and their simpler cousins, tile low-rank matrices, are well proportioned for early exascale computer architectures, which are provisioned for high processing power relative to memory capacity and memory bandwidth. They are ushering in a renaissance of computational linear algebra. A challenge is that emerging hardware architecture possesses hierarchies of its own that do not generally align with those of the algorithm. We describe modules of a software toolkit, hierarchical computations on many core architectures, that illustrate these features and are intended as building blocks of applications, such as matrix-free higher-order methods in optimization and large-scale spatial statistics. Some modules of this open-source project have been adopted in the software libraries of major vendors.

Bio: Keyes joined the Office of President Tony Chan in October 2018 as Senior Associate, with responsibilities for strategic planning and international partnerships. Keyes is also an Adjunct Professor and former Fu Foundation Chair Professor in Applied Physics and Applied Mathematics at Columbia University, and a faculty affiliate of several laboratories of the U.S. Department of Energy. He graduated summa cum laude in Aerospace and Mechanical Sciences with a certificate in Engineering Physics from Princeton in 1978, and earned a doctorate in Applied Mathematics from Harvard in 1984.