Presentation

This research school features lectures of the world-leading experts that have driven recent developments on Structure and Geometry in Matrix Computations. The participants of the school will benefit from being trained to be at the forefront of research on structured matrix and geometry-based algorithms, empowering them to make contributions to the state-of-the-art. Since this field touches upon a variety of mathematical fields, such as differential and algebraic geometry, linear algebra, numerical analysis, and optimization, the research theme of the school is a beautiful example for the need of merging seemingly distant mathematical concepts to make progress.

Structure is central to matrix computations. It often reflects properties of the underlying application, such as symmetries, and redundancy introduced during linearization or discretization processes. The exploitation of structure is often mandatory in numerical algorithms, not only to attain efficiency but also to avoid that roundoff and other errors lead to physically meaningless or spurious solutions. During the last decade significant progress has been made in this area in the context of solving polynomial systems, eigenvalue problems, and matrix equations as well as in the design of algorithms that build upon the geometry of nonlinear structures. This research school features lectures of the world-leading experts that have driven these recent developments.