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....

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Published inNumerical algorithms Vol. 93; no. 3; pp. 1401 - 1416
Main Authors Bujok, Maksymilian, Smoktunowicz, Alicja, Borowik, Grzegorz
Format Journal Article
LanguageEnglish
Published New York Springer US 01.07.2023
Springer Nature B.V
Subjects
Algebra
Algorithms
Computation
Computer Science
Decomposition
Factorization
Floating point arithmetic
Lie groups
Mathematical analysis
Matrices (mathematics)
Numeric Computing
Numerical Analysis
Original Paper
Theory of Computation
Orthogonal matrix
65L70
35A01
Condition number
65L20
65L12
Symplectic matrix
Cholesky factorization
65L10
Online AccessGet full text
ISSN1017-1398
1572-9265
1572-9265
DOI10.1007/s11075-022-01472-y

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Summary: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.
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ISSN:1017-1398
1572-9265
1572-9265
DOI:10.1007/s11075-022-01472-y