An eigen decomposition based closed-form solution for the Discrete Lyapunov and Stein Equations
Year: 2021
Type: preprint
Abstract: A simple closed-form solution to the discrete Lyapunov equation (DLE) is established for certain families of matrices. This solution is expressed in terms of the eigen decomposition (ED) for which closed-form solutions are known for all 2x2; 3x3 and certain families of matrices. For general matrices, the proposed ED based closed-form solution can be used as an efficient numerical solution when the ED can be computed. The result is then extended to give closed-form solutions for a generalization of the DLE, called the Stein equation. The proposed explicit solution's complexity is of the same order as iterative solutions and significantly smaller than known closed-form solutions. These solutions may prove convenient for analysis and synthesis problems related to these equations due to their compact form.
Source: arXiv (Cornell University)
Authors: Patel, Aaqib, Khan, Mohammed Zafar Ali
Language: English
Topic: Matrix Theory and Algorithms
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4297034596