On computing the symplectic $L{L}^T$ factorization

Abstract

We analyze two algorithms for computing the symplectic $L{L}^T$ factorization $A=L{L}^T$ of a given symmetric positive definite symplectic matrix $A$. The first algorithm $W_1$ is an implementation of the $H{H}^T$ factorization from [Dopico et al., 2009], see Theorem 5.2. The second one, algorithm $W_2$ uses both Cholesky and Reverse Cholesky decompositions of symmetric positive definite matrices. We presents a comparison of these algorithms and illustrate their properties by numerical experiments in MATLAB. A particular emphasis is given on simplecticity properties of the computed matrices in floating-point arithmetic.