Laura Grigori

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.