In the past two decades, the density matrix renormalization group (DMRG) has emerged as
an innovative new method in quantum chemistry relying on a theoretical framework very …

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

In this chapter we present numerical methods for low-rank matrix and tensor problems that
explicitly make use of the geometry of rank constrained matrix and tensor spaces. We focus …

We propose two implicit numerical schemes for the low-rank time integration of stiff
nonlinear partial differential equations. Our approach uses the preconditioned Riemannian …

Such problems as computation of spectra of spin chains and vibrational spectra of
molecules can be written as high-dimensional eigenvalue problems, ie, when the …

This thesis is concerned with numerical algorithms on matrix manifolds. It is divided into four
parts, and in all of them, we make extensive use of Riemannian geometry. The interest in …

In scientific computing and machine learning applications, matrices and more general
multidimensional arrays (tensors) can often be approximated with the help of low-rank …

Large-scale optimization problems arising from the discretization of problems involving
PDEs sometimes admit solutions that can be well approximated by low-rank matrices. In this …

In this article, a new method is proposed to approximate the rightmost eigenpair of certain
matrix-valued linear operators, in a low-rank setting. First, we introduce a suitable ordinary …

In the large scale canonical correlation analysis arising from multi-view learning
applications, one needs to compute canonical weight vectors corresponding to a few of …