The SDA Method for Numerical Solution of Lur'e Equations
  We introduce a numerical method for the numerical solution of the so-called Lur'e matrix equations that arise in balancing-related model reduction and linear-quadratic infinite time horizon optimal control. Based on the fact that the set of solutions can be characterized in terms of deflating subspaces of even matrix pencils, an iterative scheme is derived that converges linearly to the maximal solution. 
Federico Poloni and Timo Reis
math.NA