Deflating irreducible singular <em>M</em>-matrix algebraic Riccati equations

Deflating Irreducible Singular M- Matrix Algebraic Riccati Equations

A deflation technique is presented for an irreducible singular M -matrix Algebraic Riccati Equation (MARE). The technique improves the rate of convergence of a doubling algorithm, especially for an MARE in the critical case for which without deflation the doubling algorithm converges linearly and with deflation it converges quadratically. The deflation also improves the conditioning of the MARE...

On Solving Large Algebraic Riccati Matrix Equations

In this paper, we present a numerical method for solving large continuous-time algebraic Riccati equations. This method is based on the global FOM algorithm and we call it by global FOM-Riccati-Like (GFRL) algorithm .

A new two-phase structure-preserving doubling algorithm for critically singular M-matrix algebraic Riccati equations

Among numerous iterative methods for solving the minimal nonnegative solution of an M -matrix algebraic Riccati equation, the structure-preserving doubling algorithm (SDA) stands out owing to its overall efficiency as well as accuracy. SDA is globally convergent and its convergence is quadratic, except for the critical case for which it converges linearly with the linear rate 1=2. In this paper...

Order Reduction of Discrete–time Algebraic Riccati Equations with Singular Closed Loop Matrix

We study the general discrete-time algebraic Riccati equation and deal with the case where the closed loop matrix corresponding to an arbitrary solution is singular. In this case the extended symplectic pencil associated with the DARE has 0 as a characteristic root and the corresponding spectral deflating subspace gives rise to a subspace where all solutions of the DARE coincide. This allows fo...

Algebraic Riccati equations