Elementwise accurate algorithms for nonsymmetric algebraic Riccati equations associated with M-matrices

We present an elementwise accurate algorithm which incorporates the shift technique for the computation of the minimal non negative solution of a nonsymmetric algebraic Riccati equation associated to M, when M is an irreducible singular M-matrix. We propose the idea of delayed shift and some results that guarantees the applicability and the convergence of structured doubling algorithm based only on the properties of the matrix of the initial setup of doubling algorithm instead of matrix M. We provide a componentwise error analysis for the algorithm and we also show some numerical experiments that illustrate the advantage in terms of accuracy and convergence speed.