Stefano Massei (École Polytechnique Fédérale Lausanne)
Linear matrix equations, namely Sylvester and Lyapunov equations, play an important role in several applications arising in control theory and PDEs. In the large scale scenario, it is crucial to exploit the structure in the data in order to carry on the computations and store the final solution. We focus on the case in which the coefficients have off-diagonal blocks with low-rank and we study when this property is numerically preserved in the solution. Then, we propose a divide and conquer scheme able to exploit the structure, reaching a linear-polylogarithmic complexity in both time and memory consumption.