Title: Randomized Preconditioning
Speaker: Haim Avron (IBM T. J. Watson Research Center)

In this talk I will argue that when it comes to solving linear systems
or least squares problems, randomized methods are best employed as 
"preconditioners", i.e. as accelerators for iterative methods. The talk
 will discuss both dense and sparse matrices. For dense matrices, I will
 describe Blendenpik, a least-square solver for dense highly overdetermined
systems that achieves residuals similar to those of direct factorization 
based state-of-the-art solvers (LAPACK), outperforms LAPACK by large 
factors, and scales significantly better than any QR-based solver. For
sparse matrices,  I will discuss recent progress on accelerating the 
solution of sparse symmetric positive definite matrices using
randomized methods