The basics of developing numerical algorithms

In this article, we surveyed several numerical methods arising in systems and control and pointed out general principles that lead to numerically reliable algorithms for solving a large range of problems in this area. Algorithms that use orthogonal or unitary transformation were emphasized because they often lead to reliable numerical algorithms. We focused on those problems for which good algorithms are available. It is crucial to have robust numerical software available to implement these ideas, and the NICONET project aims at providing exactly that. Moreover, the underlying software library SLICOT is freely available for noncommercial use.