AN EFFICIENT AND RELIABLE IMPLEMENTATION OF THE PERIODIC QZ ALGORITHM

摘要

We discuss performance and accuracy aspects of the periodic QZ algorithm. Blocked formulations of the involved orthogonal transformations increase the data locality and thus address the first task. For the sake of reliability the proposed implementation includes balancing, implicit methods for computing shifts and carefully chosen deflation strategies. Algorithms for pole placement and other tasks arising from periodic discrete-time systems could benefit from these improvements.