Dynamic Mode Decomposition: A New Approach for Computing the DMD Modes and Eigenvalues

Abstract

In this paper we study a special case of linearly perturbed discrete-time algebraic Riccati equation. We give some sufficient conditions forthe existence of a positive definite solution of the considered equation.We propose a basic fixed point iteration and its inversion free variantfor finding a positive definite solution. Moreover, by specially choosingthe initial value in the basic fixed point iteration we prove that it con-verges to the largest solution. The theoretical results are illustratedby numerical examples.