Volker Mehrmann

Dimension Reduction of Large-Scale Systems

In the past decades, model reduction has become an ubiquitous tool in analysis and simulation of dynamical systems, control design, circuit simulation, structural dynamics, CFD, and many other disciplines dealing with complex physical models. The aim of this book is to survey some of the most successful model reduction methods in tutorial style articles and to present benchmark problems from several application areas for testing and comparing existing and new algorithms. As the discussed methods have often been developed in parallel in disconnected application areas, the intention of the mini-workshop in Oberwolfach and its proceedings is to make these ideas available to researchers and practitioners from all these different disciplines.

SLICOT—A Subroutine Library in Systems and Control Theory

This chapter describes the subroutine library SLICOT that provides Fortran 77 implementations of numerical algorithms for computations in systems and control theory. Around a nucleus of basic numerical linear algebra subroutines, this library builds methods for the design and analysis of linear control systems. A brief history of the library is given together with a description of the current version of the library and the ongoing activities to complete and improve the library in several aspects.

Vector Spaces of Linearizations for Matrix Polynomials

The classical approach to investigating polynomial eigenvalue problems is linearization, where the polynomial is converted into a larger matrix pencil with the same eigenvalues. For any polynomial there are infinitely many linearizations with widely varying properties, but in practice the companion forms are typically used. However, these companion forms are not always entirely satisfactory, and linearizations with special properties may sometimes be required. Given a matrix polynomial

Structured Polynomial Eigenvalue Problems: Good Vibrations from Good Linearizations

P

NLEVP: A Collection of Nonlinear Eigenvalue Problems

, we develop a systematic approach to generating large classes of linearizations for

Numerical methods for simultaneous diagonalization

P

Structure-Preserving Methods for Computing Eigenpairs of Large Sparse Skew-Hamiltonian/Hamiltonian Pencils

. We show how to simply construct two vector spaces of pencils that generalize the companion forms of

Balanced Truncation Model Reduction for Large-Scale Systems in Descriptor Form

P

Canonical Forms for Hamiltonian and Symplectic Matrices and Pencils

, and prove that almost all of these pencils are linearizations for

A symplectic QR like algorithm for the solution of the real algebraic Riccati equation

P