A power method for the structured singular value

Abstract

An iterative algorithm is presented to compute lower bounds for the structured singular value ( mu ). The algorithm resembles a mixture of power methods for eigenvalues and singular values, since the structured singular value can be viewed as a generalization of both. If the algorithm converges, a lower bound for mu results. The authors prove that mu is always an equilibrium point of the algorithm. However, since in general there are many equilibrium points, some heuristic ideas to achieve convergence are presented. Extensive numerical experience with the algorithm is discussed.