The Lyapunov matrix equation. Matrix analysis from a computational perspective
arXiv:1501.075649 citationsh-index: 47
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For researchers in numerical linear algebra, this provides theoretical insights and potential algorithmic improvements, but the contribution appears incremental.
The paper investigates decay properties of the solution to the Lyapunov matrix equation and discusses their use in understanding matrix properties and developing numerical solution strategies for non-low-rank, possibly sparse D.
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.