Invited Speakers

In this talk we discuss recent progress in using randomization for solving linear systems of equations and eigenvalue problems. We present first randomized versions of processes for orthogonalizing a set of vectors and their usage in the Arnoldi iteration. We then present 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.

Modern computer hardware supports an increasingly wide range of arithmetics, notably low precision floating-point ones. Lower precisions provide significant storage, communication, speed, and energy benefits that make them very attractive for high performance computing. However, they also provide a correspondingly lower accuracy. This motivates the development of mixed precision algorithms, which combine multiple precisions to achieve both high performance and high accuracy. In this talk, I will present two emerging trends in the design of mixed precision algorithms that have significant potential: modularity and adaptivity. Modularity allows for easily deriving stable mixed precision variants of an algorithm and for combining them with other types of approximations. Adaptivity allows for dynamically taking advantage of application-specific opportunities by switching the least sensitive parts of the data to low precision.