Sensitivity of the Solutions of Some Matrix Equations
نویسنده
چکیده
We develop a general method for obtaining bounds for the sensitivity of the solution of the stable Lyapunov equation. Our arguments not only work simultaneously for both the continuous and the discrete time Lyapunov equations, they work equally well for more general equations that have been studied. Further, we obtain bounds valid for all unitarily invariant norms. x 1 Introduction In this note we consider the question of the sensitivity of the solution of some linear matrix equations. The equations we consider rst are the continuous{time Lyapunov equation and the discrete{time Lyapunov equation. These are This author thanks Sonderforschungsbereich 343 "Diskrete Strukturen in der Mathematik" at the University of Bielefeld for its support and hospitality during October/November 1997 when this work was done
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