Parallel solution of large-scale algebraic Bernoulli equations with the matrix sign function method

We investigate the numerical solution of algebraic Bernoulli equations via the Newton iteration for the matrix sign function. Bernoulli equations are nonlinear matrix equations arising in control and systems theory in the context of stabilization of linear systems, coprime factorization of rational matrix-valued functions, as well as model reduction. The algorithm proposed here is easily parallelizable and thus provides an efficient tool to solve large-scale problems. We report the parallel performance and scalability of our parallel implementations on an IBM Regatta system. Efficiencies around 80% and higher are obtained for using a reduced number of nodes.