Numerical Linear Algebra Group

The SIAM Annual Meeting 2021 was held virtually, July 19 – 23, 2021. Nick Higham and I organised a two-part minisymposium “Computational Frontiers in Numerical Linear Algebra” that addressed recent algorithmic and software advances in numerical linear algebra. Links to slides from some of the talks are given below.

Minisymposium description: Numerical linear algebra (NLA) is fundamental to many applications in scientific computing. Therefore developing fast algorithms for various NLA problems is crucial to enhance our ability to tackle bigger scientific challenges. Furthermore, NLA software is used as a black box in various applications and hence theoretical guarantees on the computed results are important. Algorithmic development in NLA needs to work in tandem with the ongoing advances in computer hardware. This minisymposium will give a broad overview of various theoretical, algorithmic and software ideas that are being pursued to accelerate NLA problems.

• Part 1
  • When Floating-Point Error Matters: the Hazards and Challenges of Low-Precision Computation. Erin C. Carson, Charles University, Czech Republic. Abstract. Slides.
  • Randomization for Solving Large Systems of Linear Equations. Laura Grigori, Oleg Balabanov, and Matthias Beaupere, Inria Paris, France. Abstract.
  • Mixed Precision Algorithms for Pushing the Performance Limits of Modern HPC Architectures. Hartwig Anzt, University of Tennessee, U.S. Fritz Goebel, Thomas Gruetzmacher, and Terry Cojean, Karlsruhe Institute of Technology, Germany. Andres Tomas and Enrique S. Quintana-Orti, Universitat Politècnica de València, Spain. Abstract. Slides.
  • HeFFTe: FFT Computations Towards Exascale. Alan F. Ayala, University of Tennessee, U.S. Miroslav Stoyanov, Oak Ridge National Laboratory, U.S. Stanimire Tomov and Sebastien Cayrols, University of Tennessee, Knoxville, U.S. Jack J. Dongarra, University of Tennessee and Oak Ridge National Laboratory, U.S. Abstract. Slides.
• Part 2
  • Replacing Pivoting in Distributed Gaussian Elimination with Randomized Transforms. Neil Lindquist and Piotr Luszczek, University of Tennessee, U.S. Jack J. Dongarra, University of Tennessee and Oak Ridge National Laboratory, U.S. Abstract. Slides.
  • Data-Aware Mixed Precision Algorithms. Theo Mary, Sorbonne Universités and CNRS, France. Abstract. Slides.
  • Random Matrices Generating Large Growth in LU Factorization with Pivoting. Srikara Pranesh and Nicholas J. Higham, The University of Manchester, United Kingdom; Desmond John Higham, University of Edinburgh, United Kingdom. Abstract. Slides.
  • Mixed Precision Randomized SVD. Michael P. Connolly, Nicholas J. Higham, and Srikara Pranesh, The University of Manchester, United Kingdom. Abstract.