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.
