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 …

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 …

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 …

Usually one avoids numerical algorithms involving operations with large, fully populated
matrices. Instead one tries to reduce all algorithms to matrix-vector multiplications involving …

Large-scale problems have always been a challenge for numerical computations. An
example is the treatment of fully populated n× n matrices when n2 is close to or beyond the …

The numerical treatment of partial differential equations splits into two different parts. The
first part are the discretisation methods and their analysis. This led to the author's …

We consider large linear systems arising from the isogeometric discretization of the Poisson
problem on a single-patch domain. The numerical solution of such systems is considered a …

We present a brief survey on the modern tensor numerical methods for multidimensional
stationary and time-dependent partial differential equations (PDEs). The guiding principle of …

The usual large-scale discretizations are applied to two or three spatial dimensions. The
standard methods fail for higher dimensions because the data size increases exponentially …

The solution of time-dependent PDE-constrained optimization problems is a challenging
task in numerical analysis and applied mathematics. All-at-once discretizations and …