SR and SZ algorithms for the symplectic (butterfly) eigenproblem Original Research Article

SR and SZ algorithms for the symplectic (generalized) eigenproblem that are based on the reduction of a symplectic matrix to symplectic butterfly form are discussed. A 2n × 2n symplectic butterfly matrix has 8n − 4 (generically) nonzero entries, which are determined by 4n − 1 parameters. While the SR algorithm operates directly on the matrix entries, the SZ algorithm works with the 4n − 1 parameters. The algorithms are made more compact and efficient by using Laurent polynomials, instead of standard polynomials, to drive the iterations.