Quantum impurity models describe an atom or molecule embedded in a host material with
which it can exchange electrons. They are basic to nanoscience as representations of …

Time-dependent density-functional theory (TDDFT) describes the quantum dynamics of
interacting electronic many-body systems formally exactly and in a practical and efficient …

Matrix-product states have become the de facto standard for the representation of one-
dimensional quantum many body states. During the last few years, numerous new methods …

We show that the time-dependent variational principle provides a unifying framework for
time-evolution methods and optimization methods in the context of matrix product states. In …

The ubiquity of semilinear parabolic equations is clear from their numerous applications
ranging from physics and biology to materials and social sciences. In this paper, we …

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 …

Functions of matrices have been studied for as long as matrix algebra itself. Indeed, in his
seminal A Memoir on the Theory of Matrices (1858), Cayley investigated the square root of a …

In principle, the exponential of a matrix could be computed in many ways. Methods involving
approximation theory, differential equations, the matrix eigenvalues, and the matrix …

Approximate resolution of linear systems of differential equations with varying coefficients is
a recurrent problem, shared by a number of scientific and engineering areas, ranging from …

In this paper we consider the construction, analysis, implementation and application of
exponential integrators. The focus will be on two types of stiff problems. The first one is …