THE INTERVAL SYLVESTER EQUATION

In this paper a necessary and sufficient condition for the existence o f a solution for the interval Sylvester equation is given. A modified Oettli's inequality is derived to characterize the solution. Many dire ct methods for solving the equation are suggested and compared to each other. These methods are based on different techniques such as simula tion, linear programming, correspondence between an interval Sylvester equation and an interval linear system as well as sensitivity analysi s. An iterative technique for solving the interval Sylvester equation is provided with special conditions to guarantee the convergence. The square root of an interval matrix is calculated as an application to s olving interval Sylvester equations.