Doubling Algorithm for Nonsymmetric Algebraic Riccati Equations Based on a Generalized Transformation

We consider computing the minimal nonnegative solution of the nonsymmetric algebraic Riccati equation with M-matrix.It is well known that such equations can be efficiently solved via the structure-preserving doubling algorithm(SDA)with the shift-and-shrink transformation or the generalized Cayley transformation.In this paper,we propose a more generalized transformation of which the shift-and-shrink transformation and the generalized Cayley transformation could be viewed as two special cases.Meanwhile,the doubling algorithm based on the proposed generalized transformation is presented and shown to be well-defined.Moreover,the convergence result and the comparison theorem on convergent rate are established.Preliminary numerical experiments show that the doubling algorithm with the generalized transformation is efficient to derive the minimal nonnegative solution of nonsymmetric algebraic Riccati equation with M-matrix.