Numerical Linear Algebra Group

Erin Carson, Nick Higham, and Theo Mary organized a double minisymposium “Mixed Precision Algorithms in Numerical Linear Algebra” (Part I, Part II) at the SIAM Conference on Computational Science and Engineering (CSE23), which took place in Amsterdam on February 26 – March 3, 2023.

Minisymposium abstract: The increasing support of lower precision arithmetics in hardware provides new opportunities for high performance scientific computing. However, even though low precision arithmetics can provide significant speed, communication, and energy benefits, their use in scientific computing poses the challenge of preserving the accuracy and stability of the computation. To address this issue, a variety of mixed precision algorithms that combine low and high precisions have emerged. This MS will discuss recent advances in mixed precision algorithms for a broad range of numerical linear algebra computations, including matrix multiplication, matrix factorizations, iterative solvers, least-square problems, and matrix and tensor low-rank approximations.

Below we provide the slides of the ten talks that were delivered during this minisymposium.

• Erin C. Carson (Charles University), Mixed Precision Randomized Preconditioners.
• Mantas Mikaitis (University of Leeds), Monotonicity of Multi-Term Floating-Point Adders.
• Ichi Yamazaki (Sandia National Laboratories), A New Mixed-Precision Benchmark for HP Computers.
• Eda Oktay (Charles University), Solving Total Least Squares Problems Using Mixed Precision.
• Ian McInerney (The University of Manchester), Chopblas: Simulating Mixed-Precision and Stochastically Rounded Linear Algebra.
• Yuhsiang M. Tsai (Karlsruhe Institute of Technology), Mixed Precision Algebraic Multigrid on GPUs.
• Roméo Molina (Sorbonne Université), Adaptive Precision Sparse Iterative Solvers.
• Daniel R. Bielich (University of Tennessee), Mixed Precision in Pivoting Avoiding QR.
• Matthieu Robeyns (Université Paris Saclay), Mixed Precision Iterative Refinement for Low-Rank Matrix and Tensor Approximations.
• Takeshi Fukaya (Hokkaido University), An Attempt of Exploiting Low Precision Computing in the GMRES(m) Method.