Backward Perturbation Analysis of the Periodic Discrete-Time Algebraic Riccati Equation

Abstract

Abstract. Normwise backward errors and residual bounds for an approximate Hermitian positive semidefinite solution set to the periodic discrete-time algebraic Riccati equation are obtained. The results are illustrated by using simple numerical examples.

Solvability Theory and Iteration Method for One Self-Adjoint Polynomial Matrix Equation

“…Many numerical methods have been proposed, such as invariant subspace methods [6], Schur method [7], doubling algorithm [8], and structure-preserving doubling algorithm [9,10]. At the same time the perturbation theory was developed in [11][12][13][14][15], as well as the unified methods for the discrete-time and continuous-time algebraic Riccati equations [16,17]. A general iteration method for (1) given in this paper can be seen as a new algorithm for the algebraic Riccati equation 2, setting = 2 and = 1.…”