SR and SZ algorithms for the symplectic (butterfly) eigenproblem

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 x 2n symplectic butterfly matrix has 8n - 4 (generical ly) nonzero entries, which are determined by 4n - 1 parameters. While the S R algorithm operates directly on the matrix entries, the SZ algorithm works with the 4n - 1 parameters. The algorithms are made more compact and effic ient by using Laurent polynomials, instead of standard polynomials, to driv e the iterations. (C) 1999 Elsevier Science Inc. All rights reserved.