On some Krylov subspace based methods for large-scale nonsymmetric algebraic Riccati problems

In the present paper, we consider large scale nonsymmetric matrix Riccati equations with low rank right hand sides. These matrix equations appear in many applications such as transport theory, Wiener–Hopf factorization of Markov chains, applied probability and others. We show how to apply directly Krylov methods such as the extended block Arnoldi algorithm to get low rank approximate solutions. We also combine the Newton method and block Krylov subspace methods to get approximations of the desired minimal nonnegative solution. We give some theoretical results and report some numerical experiments for the well known transport equation.