Randomized methods for matrix computations

The purpose of this text is to provide an accessible introduction to a set of recently developed algorithms for factorizing matrices. These new algorithms attain high practical speed by reducing the dimensionality of intermediate computations using randomized projections. The algorithms are particularly powerful for computing low-rank approximations to very large matrices, but they can also be used to accelerate algorithms for computing full factorizations of matrices. A key competitive advantage of the algorithms described is that they require less communication than traditional deterministic methods

Efficient Algorithms for CUR and Interpolative Matrix Decompositions

The manuscript describes efficient algorithms for the computation of the CUR and ID decompositions. The methods used are based on simple modifications to the classical truncated pivoted QR decomposition, which means that highly optimized library codes can be utilized for implementation. For certain applications, further acceleration can be attained by incorporating techniques based on randomized projections. Numerical experiments demonstrate advantageous performance compared to existing techniques for computing CUR factorizations