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 …

This book started as a set of lectures in computational science for inverse problems where
electromagnetics was used as an example. Talking with many graduate students and other …

Fractional differential equations are becoming increasingly used as a modelling tool for
processes associated with anomalous diffusion or spatial heterogeneity. However, the …

The rational Krylov space is recognized as a powerful tool within model order reduction
techniques for linear dynamical systems. However, its success has been hindered by the …

Matrix functions are a central topic of linear algebra, and problems of their numerical
approximation appear increasingly often in scientific computing. We review various rational …

A computational method is given for solving the forward modelling problem for transient
electromagnetic exploration. Its key features are the discretization of the quasi-static …

Airborne time-domain electromagnetic surveys are effective tools for mineral exploration and
geologic map**. 3D inversion of airborne electromagnetic data is a challenging …

A novel parallel algorithm for the integration of linear initial-value problems is proposed. This
algorithm is based on the simple observation that homogeneous problems can typically be …

A new rational Krylov method for the efficient solution of nonlinear eigenvalue problems,
A(λ)x=0, is proposed. This iterative method, called fully rational Krylov method for nonlinear …

In this article we investigate model order reduction of large-scale systems using time-limited
balanced truncation, which restricts the well known balanced truncation framework to …