Mixed Precision Randomised Nyström Method

Randomised methods are often employed to obtain low-rank approximations of large matrices. These methods have a relatively small computational cost, which can be further reduced by performing some of the computations in lower precision. In this work, we consider a single pass version of a randomised Nyström method for approximating a symmetric positive semidefinite matrix A. This method accesses A only once to compute a matrix-matrix product. We perform this product in lower than the working precision and examine the finite precision error. The Nyström approximation is then used to construct a limited memory preconditioner for systems with coefficient matrices with spectral decay and we solve these via conjugate gradient method.