The computational solution of problems can be restricted by the availability of solution
methods for linear (ized) systems of equations. In conjunction with iterative methods …

When simulating a mechanism from science or engineering, or an industrial process, one is
frequently required to construct a mathematical model, and then resolve this model …

Our times can be characterized by, among many other attributes, the seemingly increasing
speed of everything. Within science, it has led to the publication explosion, which reflects the …

The solution of quadratic or locally quadratic extremum problems subject to linear (ized)
constraints gives rise to linear systems in saddle point form. This is true whether in the …

In IMA J. Numer. Anal., 29 (2009), pp. 24--42, Nielsen, Tveito, and Hackbusch study the
operator generated by using the inverse of the Laplacian as the preconditioner for second …

Computationally solving an optimisation problem on Hilbert spaces requires discretisation
and the application of an optimisation method to the resulting finite-dimensional problem. In …

The conjugate gradient method (CG) for solving linear systems of algebraic equations
represents a highly nonlinear finite process. Since the original paper of Hestenes and Stiefel …

We propose and analyze two strategies for preconditioning linear operator equations that
arise in PDE constrained optimal control in the framework of conjugate gradient methods …

From meteorology to medical imaging and cell mechanics, many scientific domains use
inverse problems (IPs) to extract physical measurements from image movement. To this end …

Regularization robust preconditioners for PDE-constrained optimization problems have
been successfully developed. These methods, however, typically assume observation data …