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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| Veröffentlicht in: | Numerical algorithms 2023-07, Vol.93 (3), p.1401-1416 |
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| container_title | Numerical algorithms |
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| creator | Bujok, Maksymilian Smoktunowicz, Alicja Borowik, Grzegorz |
| description | 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. |
| doi_str_mv | 10.1007/s11075-022-01472-y |
| format | Article |
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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.</description><identifier>ISSN: 1017-1398</identifier><identifier>EISSN: 1572-9265</identifier><identifier>DOI: 10.1007/s11075-022-01472-y</identifier><language>eng</language><publisher>New York: Springer US</publisher><subject>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</subject><ispartof>Numerical algorithms, 2023-07, Vol.93 (3), p.1401-1416</ispartof><rights>The Author(s) 2022</rights><rights>The Author(s) 2022. This work is published under http://creativecommons.org/licenses/by/4.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c244t-a3e40688c9a5aa604b2fd7466b25e73f378072885d9f4f272d270c4106a596213</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s11075-022-01472-y$$EPDF$$P50$$Gspringer$$Hfree_for_read</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s11075-022-01472-y$$EHTML$$P50$$Gspringer$$Hfree_for_read</linktohtml><link.rule.ids>314,780,784,27923,27924,41487,42556,51318</link.rule.ids></links><search><creatorcontrib>Bujok, Maksymilian</creatorcontrib><creatorcontrib>Smoktunowicz, Alicja</creatorcontrib><creatorcontrib>Borowik, Grzegorz</creatorcontrib><title>On computing the symplectic LLT factorization</title><title>Numerical algorithms</title><addtitle>Numer Algor</addtitle><description>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.</description><subject>Algebra</subject><subject>Algorithms</subject><subject>Computation</subject><subject>Computer Science</subject><subject>Decomposition</subject><subject>Factorization</subject><subject>Floating point arithmetic</subject><subject>Lie groups</subject><subject>Mathematical analysis</subject><subject>Matrices (mathematics)</subject><subject>Numeric Computing</subject><subject>Numerical Analysis</subject><subject>Original Paper</subject><subject>Theory of Computation</subject><issn>1017-1398</issn><issn>1572-9265</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2023</creationdate><recordtype>article</recordtype><sourceid>C6C</sourceid><sourceid>AFKRA</sourceid><sourceid>AZQEC</sourceid><sourceid>BENPR</sourceid><sourceid>CCPQU</sourceid><sourceid>DWQXO</sourceid><sourceid>GNUQQ</sourceid><recordid>eNp9kLFOwzAURS0EEqXwA0yRmA3PL47tjKgCihSpS5kt17VLqjYJtjuEr8cQJDamd4d77pMOIbcM7hmAfIiMgawoIFJgXCIdz8iMVTnUKKrznIFJyspaXZKrGPcAGUM5I3TVFbY_DqfUdrsivbsijsfh4GxqbdE068Ibm_rQfprU9t01ufDmEN3N752Tt-en9WJJm9XL6-KxoRY5T9SUjoNQytamMkYA36DfSi7EBisnS19KBRKVqra15x4lblGC5QyEqWqBrJyTu2l3CP3HycWk9_0pdPmlxpopAbWQkFs4tWzoYwzO6yG0RxNGzUB_a9GTFp216B8tesxQOUExl7udC3_T_1BfHpdjgg</recordid><startdate>20230701</startdate><enddate>20230701</enddate><creator>Bujok, Maksymilian</creator><creator>Smoktunowicz, Alicja</creator><creator>Borowik, Grzegorz</creator><general>Springer US</general><general>Springer Nature B.V</general><scope>C6C</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>8FE</scope><scope>8FG</scope><scope>ABJCF</scope><scope>AFKRA</scope><scope>ARAPS</scope><scope>AZQEC</scope><scope>BENPR</scope><scope>BGLVJ</scope><scope>CCPQU</scope><scope>DWQXO</scope><scope>GNUQQ</scope><scope>HCIFZ</scope><scope>JQ2</scope><scope>K7-</scope><scope>L6V</scope><scope>M7S</scope><scope>P62</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PTHSS</scope></search><sort><creationdate>20230701</creationdate><title>On computing the symplectic LLT factorization</title><author>Bujok, Maksymilian ; Smoktunowicz, Alicja ; Borowik, Grzegorz</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c244t-a3e40688c9a5aa604b2fd7466b25e73f378072885d9f4f272d270c4106a596213</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2023</creationdate><topic>Algebra</topic><topic>Algorithms</topic><topic>Computation</topic><topic>Computer Science</topic><topic>Decomposition</topic><topic>Factorization</topic><topic>Floating point arithmetic</topic><topic>Lie groups</topic><topic>Mathematical analysis</topic><topic>Matrices (mathematics)</topic><topic>Numeric Computing</topic><topic>Numerical Analysis</topic><topic>Original Paper</topic><topic>Theory of Computation</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Bujok, Maksymilian</creatorcontrib><creatorcontrib>Smoktunowicz, Alicja</creatorcontrib><creatorcontrib>Borowik, Grzegorz</creatorcontrib><collection>SpringerOpen</collection><collection>CrossRef</collection><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>Materials Science & Engineering Collection</collection><collection>ProQuest Central</collection><collection>Advanced Technologies & Aerospace Collection</collection><collection>ProQuest Central Essentials</collection><collection>ProQuest Central</collection><collection>Technology Collection</collection><collection>ProQuest One Community College</collection><collection>ProQuest Central Korea</collection><collection>ProQuest Central Student</collection><collection>SciTech Premium Collection</collection><collection>ProQuest Computer Science Collection</collection><collection>Computer Science Database</collection><collection>ProQuest Engineering Collection</collection><collection>ProQuest Engineering Database</collection><collection>ProQuest Advanced Technologies & Aerospace Collection</collection><collection>ProQuest One Academic Eastern Edition (DO NOT USE)</collection><collection>ProQuest One Academic</collection><collection>ProQuest One Academic UKI Edition</collection><collection>Engineering Collection</collection><jtitle>Numerical algorithms</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Bujok, Maksymilian</au><au>Smoktunowicz, Alicja</au><au>Borowik, Grzegorz</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>On computing the symplectic LLT factorization</atitle><jtitle>Numerical algorithms</jtitle><stitle>Numer Algor</stitle><date>2023-07-01</date><risdate>2023</risdate><volume>93</volume><issue>3</issue><spage>1401</spage><epage>1416</epage><pages>1401-1416</pages><issn>1017-1398</issn><eissn>1572-9265</eissn><abstract>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.</abstract><cop>New York</cop><pub>Springer US</pub><doi>10.1007/s11075-022-01472-y</doi><tpages>16</tpages><oa>free_for_read</oa></addata></record> |
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| ispartof | Numerical algorithms, 2023-07, Vol.93 (3), p.1401-1416 |
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| language | eng |
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| 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 |
| title | On computing the symplectic LLT factorization |
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