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

Abstract

A deflation technique is presented for an irreducible singular Mmatrix 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 in the critical case and thus enables its minimal nonnegative solution to be computed more accurately.

A POD projection method for large-scale algebraic Riccati equations

“…A large amount of recent research has been devoted to the development and analysis of algorithms for large-scale AREs; see the recent survey [15]. Many of the approaches are inspired by computational linear algebra methods and include Krylov subspace methods in a projection framework [58,38,39,40,36,61], ADI methods [13,14,15], subspace iterations [50,16], and doubling methods [49,72,73].…”