On computing the symplectic LLT factorization

Autor: Maksymilian Bujok, Alicja Smoktunowicz, Grzegorz Borowik
Rok vydání: 2022
Předmět:
Zdroj: Numerical Algorithms.
ISSN: 1572-9265
1017-1398
Popis: We analyze two algorithms for computing the symplectic factorization A = LLT of a given symmetric positive definite symplectic matrix A. The first algorithm W1 is an implementation of the HHT 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 W2 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.
Databáze: OpenAIRE
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