### Daniel Kressner, Volker Mehrmann and Thilo Penzl

SLICOT Working Note 1999-7: June 1999.

This paper describes the benchmark collection DTLEX, that contains test examples of discrete-time algebraic Lyapunov equations. These matrix equations are also known as Stein equations. The main focus of DTLEX is on scalable benchmark examples depending on parameters, which affect the conditioning of the equation. Such examples are particularly useful for the assessment of the complexity and the accuracy of numerical solution methods.