Randomization techniques for large scale linear algebra

This talk will discuss several recent advances in using randomization and communication avoiding techniques for solving large scale linear algebra operations. It will focus in particular on solving linear systems of equations, eigenvalue problems, and computing the low rank approximation of a large matrix. In the context of linear systems of equations, we discuss a randomized Gram-Schmidt process and show that it is efficient as classical Gram-Schmidt and numerically stable as modified Gram-Schmidt.  We exploit the usage of mixed precision in this context and discuss its usage in linear solvers. We then discuss a block orthogonalization method and its usage for solving eigenvalue problems. We also address the problem of preconditioning. The usage of these methods in challening application is further discussed.