On computing the symplectic LL^T factorization

04/08/2022

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by   Maksymilian Bujok, et al.

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We analyze two algorithms for computing the symplectic LL^T 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 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.