Low-rank tensor representations can provide highly compressed approximations of
functions. These concepts, which essentially amount to generalizations of classical …

In various engineering and applied science applications, repetitive numerical simulations of
partial differential equations (PDEs) for varying input parameters are often required (eg …

Schatten p-quasi-norm minimization has advantages over nuclear norm minimization in
recovering low-rank matrices. However, Schatten p-quasi-norm minimization is much more …

We study an iterative low-rank approximation method for the solution of the steady-state
stochastic Navier--Stokes equations with uncertain viscosity. The method is based on …

We study efficient solution methods for stochastic eigenvalue problems arising from
discretization of self-adjoint PDEs with random data, where the underlying operators depend …

We present a reduced basis stochastic Galerkin method for partial differential equations with
random inputs. In this method, the reduced basis methodology is integrated into the …

We study a multigrid method for solving large linear systems of equations with tensor
product structure. Such systems are obtained from stochastic finite element discretization of …

This paper is devoted to designing fast solvers and efficient preconditioners for the optimal
control problems (OCPs) constrained by stochastic fractional elliptic equations. We first …

A preconditioning strategy is proposed for the iterative solve of large numbers of linear
systems with variable matrix and right-hand side which arise during the computation of …

In this paper, we introduce and analyze a new low-rank multilevel strategy for the solution of
random diffusion problems. Using a standard stochastic collocation scheme, we first …