Improving the Convergence of the Periodic QZ Algorithm. ICINCO 2019
No Thumbnail Available
The periodic QZ algorithm involved in the structure-preserving skew-Hamiltonian/Hamiltonian algorithm is investigated. These are key algorithms for many applications in diverse theoretical and practical domains such as periodic systems, (robust) optimal control, and characterization of dynamical systems. Although in use for several years, few examples of skew-Hamiltonian/Hamiltonian eigenproblems have been discovered for which the periodic QZ algorithm either did not converge or required too many iterations to reach the solution. This paper investigates this rare bad convergence behavior and proposes some modifications of the periodic QZ and skew-Hamiltonian/Hamiltonian solvers to avoid nonconvergence failures and improve the convergence speed. The results obtained on a generated set of one million skew-Hamiltonian/Hamiltonian eigenproblems of order 80 show no failures and a significant reduction (sometimes of over 240 times) of the number of iterations.
Eigenvalue Problem, Hamiltonian Matrix, Numerical Methods, Optimal Control