The Lyapunov matrix equation. Matrix analysis from a computational perspective

Abstract

Decay properties of the solution $X$ to the Lyapunov matrix equation $AX+X{A}^T=D$ are investigated. Their exploitation in the understanding of equation matrix properties, and in the development of new numerical solution strategies when $D$ is not low rank but possibly sparse is also briefly discussed.

This work is a contribution to the Seminar series "Topics in Mathematics", of the PhD Program of the Mathematics Department, Università di Bologna, Italy

References in corpus (1)

• Sparse solution of the Lyapunov equation for large-scale interconnected systems

Cited by in corpus (3)

• Sparsity Preserving Optimal Control of Discretized PDE Systems
• Iterative methods for the delay Lyapunov equation with T-Sylvester preconditioning
• Sparse solution of the Lyapunov equation for large-scale interconnected systems