Advanced Numerical Methods: State-of-the-Art Algorithms for Systems and Control

March 17, 2003--Advanced Numerical Methods is a new Mathematica application package that expands the functionality of Control System Professional with an extensive collection of state-of-the-art numerical algorithms. Combined with Mathematica's extensive graphical capabilities and automatic arbitrary-precision control, Advanced Numerical Methods provides a superior environment for solving industrial and research control problems.

Advanced Numerical Methods is the result of the collaboration of Wolfram Research with Biswa Nath Datta, IEEE Fellow and Presidential Research Professor at Northern Illinois University, and Daniil Sarkissian, Assistant Professor of Mathematics at Mississippi State University. Seamlessly integrated into the Control System Professional Suite framework, Advanced Numerical Methods offers a variety of algorithms for each problem. Users can choose the most appropriate tool for a given task or have the package choose a suitable method automatically based on the size of the problem and the accuracy required.

New algorithms include:

• The Schur and Hessenberg-Schur methods for the Lyapunov and Sylvester matrix equations
• The Schur, Newton, matrix-sign function, and inverse-free methods for solving the algebraic Riccati equations
• The block-Hessenberg forms and Cholesky factors of the controllability and observability Gramians
• The recursive, explicit QR, Schur, and other algorithms for pole assignment as well as the projection technique for partial pole assignment
• Constrained feedback stabilization using the pole assignment and Lyapunov algorithms
• The design of the reduced-order state estimator and model reduction via an extensive library of algorithms
• System identification using the Markov parameters, the subspace methods, and the frequency-domain methods
• Algorithms for the generalized matrix eigenvalue problem, the generalized Schur decomposition, and the ordered Schur and generalized Schur decompositions

For more information, see the Advanced Numerical Methods product pages.