On computing the symplectic LLT factorization

We analyze two algorithms for computing the symplectic factorization A = LL T of a given symmetric positive definite symplectic matrix A . The first algorithm W 1 is an implementation of the HH T factorization from Dopico and Johnson ( SIAM J. Matrix Anal. Appl. 31(2):650–673, 2009 ), see Theorem 5.2. The second one is a new algorithm W 2 that uses both Cholesky and Reverse Cholesky decompositions of symmetric positive definite matrices. We present a comparison of these algorithms and illustrate their properties by numerical experiments in MATLAB . A particular emphasis is given on symplecticity properties of the computed matrices in floating-point arithmetic.