Laura Grigori
Laura Grigori is a Professor at EPFL and former Director of Research at Inria, where she led the Alpines team. Her research focuses on numerical linear algebra, communication-avoiding algorithms, and scalable solvers for scientific computing. She has made influential contributions to high-performance computing with applications in physics and engineering.
Session
Randomization is a powerful dimensionality reduction technique that allows to solve large scale problems while leveraging optimized kernels and enabling the usage of mixed precision. In this talk we will review recent progress in using randomization for solving linear systems of equations or eigenvalue problems. We first discuss sketching techniques that allow to embed large-dimensional subspaces while preserving geometrical properties and their parallel implementations. We then present randomized versions of processes for orthogonalizing a set of vectors and their usage in the Arnoldi iteration. We discuss associated Krylov subspace methods for solving large-scale linear systems of equations and eigenvalue problems. The new methods retain the numerical stability of classic Krylov methods while reducing communication and being more efficient on modern massively parallel computers. We finally discuss their implementation in a Julia library.