Given the square matrices A,B,D,E and the matrix C of conforming dimensions, we consider
the linear matrix equation A\mathbfXE+D\mathbfXB=C in the unknown matrix \mathbfX. Our …

We consider the numerical solution of elliptic partial differential equations with random
coefficients. Such problems arise, for example, in uncertainty quantification for groundwater …

The quantification of probabilistic uncertainties in the outputs of physical, biological, and
social systems governed by partial differential equations with random inputs require, in …

Much attention has recently been devoted to the development of Stochastic Galerkin (SG)
and Stochastic Collocation (SC) methods for uncertainty quantification. An open and …

In this work we propose and analyze a weighted reduced basis method to solve elliptic
partial differential equations (PDEs) with random input data. The PDEs are first transformed …

We investigate the structural, spectral, and sparsity properties of Stochastic Galerkin
matrices as they arise in the discretization of linear differential equations with random …

The discretization of linear partial differential equations with random data by means of the
stochastic Galerkin finite element method results in general in a large coupled linear system …

In this article we introduce new methods for the analysis of high dimensional data in tensor
formats, where the underling data come from the stochastic elliptic boundary value problem …

We propose a method for the construction of preconditioners of parameter-dependent
matrices for the solution of large systems of parameter-dependent equations. The proposed …

We apply polynomial approximation methods—known in the numerical PDEs context as
spectral methods—to approximate the vector-valued function that satisfies a linear system of …