Today, numerical computations play a crucial role in the study of complex physical, biological, and technical systems by simulating these systems in detail and in their full complexity, because it is often impossible or too expensive to analyze such systems by experiments (for example, airplane crashes).

At the heart of these experiments we generally need to solve (sequences of) very large nonlinear and linear systems of equations and eigenvalue problems. The solution of these systems are needed to evolve complex systems over time and to study their stability. Given the large size of the problems involved and their computational complexity, the implementation of high performance solution techniques on large parallel computers plays an important role as well.

In the first part of the presentation we will discuss several applications from which interesting numerical analysis problems arise. In the second part we will discuss several research issues and some of our recent advances in the solution of very large (non)linear systems and eigenvalue problems.