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Explore the world of mixed-precision computing in this 58-minute seminar presented by Théo Mary from Sorbonne University. Dive into the benefits and challenges of using lower precision arithmetic in high-performance computing, and discover how mixed-precision algorithms combine multiple precisions to achieve both high performance and accuracy. Learn about three key themes in mixed-precision computing: refinement, modularity, and adaptivity. Understand how refinement allows for low-precision computations with high-accuracy results, how modularity enables the creation of new mixed-precision algorithm variants, and how adaptivity dynamically optimizes precision based on application-specific needs. Gain insights from a CNRS researcher specializing in high-performance parallel numerical algorithms, with a focus on accelerating linear algebra computations through numerical approximations.