During the last years, low‐rank tensor approximation has been established as a new tool in
scientific computing to address large‐scale linear and multilinear algebra problems, which …

In the past decades, Model Order Reduction (MOR) has demonstrated its robustness and
wide applicability for simulating large-scale mathematical models in engineering and the …

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 …

The matrix completion problem consists of finding or approximating a low-rank matrix based
on a few samples of this matrix. We propose a new algorithm for matrix completion that …

In recent years, compressed sensing (CS) has attracted considerable attention in areas of
applied mathematics, computer science, and electrical engineering by suggesting that it may …

Efficient numerical algorithms for the solution of large and sparse matrix Riccati and
Lyapunov equations based on the low rank alternating directions implicit (ADI) iteration have …

We extend results on the dynamical low-rank approximation for the treatment of time-
dependent matrices and tensors (Koch and Lubich; see [SIAM J. Matrix Anal. Appl., 29 …

Matrices of low rank can be uniquely determined from fewer linear measurements, or
entries, than the total number of entries in the matrix. Moreover, there is a growing literature …

The aim of this paper is to derive convergence results for projected line-search methods on
the real-algebraic variety M_≤k of real m*n matrices of rank at most k. Such methods extend …

In this paper, the differential geometry of the novel hierarchical Tucker format for tensors is
derived. The set HT, k of tensors with fixed tree T and hierarchical rank k is shown to be a …