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arXiv · 2204.03927

On computing the symplectic $LL^T$ factorization

Maksymilian Bujok·Alicja Smoktunowicz·Grzegorz Borowik
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Abstract

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.

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Maksymilian Bujok, Alicja Smoktunowicz, Grzegorz Borowik. 2022-04-08. On computing the symplectic $LL^T$ factorization. https://arxiv.org/abs/2204.03927

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