Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8902291 | Journal of Computational and Applied Mathematics | 2018 | 11 Pages |
Abstract
The T-congruence Sylvester equation is the matrix equation AX+XTB=C, where AâRmÃn, BâRnÃm and CâRmÃm are given, and matrix XâRnÃm is to be determined. The T-congruence Sylvester equation has recently attracted attention because of a relationship with palindromic eigenvalue problems. For example, necessary and sufficient conditions for the existence and uniqueness of solutions, and numerical solvers have been intensively studied. In this paper, we will show that, under a certain condition and n=m, the T-congruence Sylvester equation can be transformed into the Lyapunov equation. This may lead to further properties and efficient numerical solvers by utilizing the rich literature on the Lyapunov equation.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Applied Mathematics
Authors
Masaya Oozawa, Tomohiro Sogabe, Yuto Miyatake, Shao-Liang Zhang,