{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,26]],"date-time":"2026-02-26T20:40:58Z","timestamp":1772138458021,"version":"3.50.1"},"reference-count":9,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2022,12,11]],"date-time":"2022-12-11T00:00:00Z","timestamp":1670716800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2022,12,11]],"date-time":"2022-12-11T00:00:00Z","timestamp":1670716800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Numer Algor"],"published-print":{"date-parts":[[2023,7]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We analyze two algorithms for computing the symplectic factorization <jats:bold><jats:italic>A<\/jats:italic><\/jats:bold> = <jats:bold><jats:italic>LL<\/jats:italic><\/jats:bold><jats:sup><jats:bold><jats:italic>T<\/jats:italic><\/jats:bold><\/jats:sup> of a given symmetric positive definite symplectic matrix <jats:bold><jats:italic>A<\/jats:italic><\/jats:bold>. The first algorithm <jats:bold><jats:italic>W<\/jats:italic><\/jats:bold><jats:sub><jats:bold>1<\/jats:bold><\/jats:sub> is an implementation of the <jats:bold><jats:italic>HH<\/jats:italic><\/jats:bold><jats:sup><jats:italic>T<\/jats:italic><\/jats:sup> factorization from Dopico and Johnson (<jats:italic>SIAM J. Matrix Anal. Appl.<\/jats:italic> 31(2):650\u2013673, 2009), see Theorem 5.2. The second one is a new algorithm <jats:bold><jats:italic>W<\/jats:italic><\/jats:bold><jats:sub><jats:bold>2<\/jats:bold><\/jats:sub> 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 <jats:italic>MATLAB<\/jats:italic>. A particular emphasis is given on symplecticity properties of the computed matrices in floating-point arithmetic.<\/jats:p>","DOI":"10.1007\/s11075-022-01472-y","type":"journal-article","created":{"date-parts":[[2022,12,11]],"date-time":"2022-12-11T04:16:16Z","timestamp":1670732176000},"page":"1401-1416","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["On computing the symplectic LLT factorization"],"prefix":"10.1007","volume":"93","author":[{"given":"Maksymilian","family":"Bujok","sequence":"first","affiliation":[]},{"given":"Alicja","family":"Smoktunowicz","sequence":"additional","affiliation":[]},{"given":"Grzegorz","family":"Borowik","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2022,12,11]]},"reference":[{"key":"1472_CR1","doi-asserted-by":"publisher","first-page":"260","DOI":"10.1016\/j.aml.2006.04.004","volume":"20","author":"M Benzi","year":"2007","unstructured":"Benzi, M., Razouk, N.: On the Iwasawa decomposition of a symplectic matrix. 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Linear Algebra Appl. 302\u2013303, 469\u2013533 (1999). https:\/\/doi.org\/10.1016\/S0024-3795(99)00191-3","journal-title":"Linear Algebra Appl."},{"key":"1472_CR9","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/S0024-3795(03)00370-7","volume":"368","author":"H Xu","year":"2003","unstructured":"Xu, H.: An SVD-like matrix decomposition and its applications. 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