Special Matrix Problems in Signals, Systems and Control

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During the last few decades linear algebra has played a fundamental role in advances being made in the area of signals, systems and control. The most profound impact has been in the computational and implementational aspects, where numerical linear algebraic algorithms have strongly influenced the ways in which problems are being solved. The advent of special computing architectures such as vector processors and distributed processor arrays has also emphasized parallel and real-time processing of basic linear algebra modules for these application areas. This project is about numerical linear algebra and applications in signals, systems and control, with special emphasis on implementation aspects on parallel architectures. The focus is on "special matrix" problems, i.e. matrices which are either sparse, patterned or structured. For such matrices appropriate definitions of numerical stability and sensitivity have recently been introduced. Numerical methods for the above application areas ought to be numerically stable in this restricted sense and at the same time ought to exploit the structure of the matrices to improve computational complexity and parallelizability. This will be applied to challenging problems in these areas such as target tracking, robust control and model reduction of large scale plants.