AN EXPLORATORY-STUDY OF A SUBSPACE ITERATION METHOD AS AN ALTERNATIVE TO THE QR METHOD FOR FLOQUET EIGENANALYSIS

Floquet eigenanalysis requires a few dominant eigenvalues of the Floquet transition matrix (FTM). Although the QR method is used almost exclusively, it is expensive for such partial eigenanalysis; the operation counts and, thereby, the approximate machine-time grow cubically with the matrix order. Accordingly, for Floquet eigenanalysis, the Arnoldi-Saad method, a subspace iteration method, is investigated as an alternative to the QR method. The two methods are compared for machine-time efficiency and computational reliability, which is quantified by the condition numbers of the required eigenvalues and the residual errors of the corresponding eigenpairs. The Arnoldi-Saad method takes much less machine-time than the QR method with comparable computational reliability and offers promise for large-scale Floquet eigenanalysis (say, FTM order > 100).