In addition to the theoretical exploration of new mathematical methods for solving linear systems, matrix equations and problems in model order reduction or optimal control, we endeavor to create experimental as well as production implementations of our algorithms in software packages. The main focus is on the one hand to create reproducible results and on the other hand to make use of modern computer architectures and their programming models. Depending on the problem, we use one of the common programming languages in scientific computing. These range from C / C++ and MATLAB to Fortran and Python in our research group and include complex projects that include several of those languages.
RRQR-MEX provides a MATLAB routine rrqr, implementing an interface to the FORTRAN RRQR codes by G. Quintana-Orti und C.H. Bischof.
THIS IS PROVIDED FOR REPRODUCIBILITY ONLY.
In recent Matlab on modern multicore CPUs we recommend qr(.,0) or svd based solutions. This is similarly robust, but usually much faster due to the lack of parallelism in the original Fortran codes.
PLiCMR is a library of routines for parallel model reduction of large-scale discrete or continuous linear time invariant systems represented using the state-space model. Three methods are available in PLiCMR: Balance & Truncate, Singular Perturbation Approximation, and Hankel-Norm Approximation. Future extensions will include Balanced Stochastic Truncation.
The Hamiltonian Eigenvalue Problem occurs in many areas of Systems and Control theory. One of the main applications is the solution of the algebraic Riccati equation. We collect a set of FORTRAN 77 and MATALB Codes to solve this Eigenvalue problem and as well as the Riccati Equation.
An implementation of the elliptic integral based (sub)optimal alternating directions implicit (ADI) shift parameters following the theory by Wachspress et. al.