Optimal symplectic Householder transformations for SR decomposition

The SR factorization is a key step for some important structure-preserving eigenproblems. In this work, we introduce symplectic Householder transformations and show their main features. Furthermore, we construct a new algorithm for computing the SR factorization, based on these transformations. The new algorithm is the analogous of the classical QR factorization, via Householder transformations. Unlike the latter, it involves free parameters. We show how to choose these parameters in an optimal way and derive an algorithm implementing this. Some illustrating numerical experiments, comparisons and computational aspects are given.