Backard Error Analysis of the Matrix Equations for Sylvester and Lyapunov
Sylvester与Lyapunov方程向后误差分析

The normwise backward errors of the approximate solutions to the Sylvester equation $AX+YB=C$ and Lyapunov equation $A^{\rm T} X+XA=-Q,(Q >0)$ are evaluated, and upper and lower bounds are also obtained. These results improve the existing results.