Algebraic method for LU decomposition of dual quaternion matrix and its corresponding structure-preserving algorithm

Due to the increasing applications of dual quaternion and their matrices in recent years, as well as the significance of LU decomposition as a matrix decomposition technique, in this paper, we propose dual quaternion Gaussian transformation and obtain dual quaternion LU decomposition by using Gaussi...

Full description

Saved in:
Bibliographic Details
Published in:Numerical algorithms 2024-11, Vol.97 (3), p.1367-1382
Main Authors: Wang, Tao, Li, Ying, Wei, Musheng, Xi, Yimeng, Zhang, Mingcui
Format: Article
Language:English
Subjects:
Algebra
Algorithms
Computer Science
Coordinate transformations
Decomposition
Numbers
Numeric Computing
Numerical Analysis
Original Paper
Quaternions
Robots
Theory of Computation
Transformations (mathematics)
Citations: Items that this one cites
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
cited_by
cites cdi_FETCH-LOGICAL-c270t-8511bb95c0ef7e478e08a49f07254de43863a8b5bce75ca4ad8b9e76711b6673
container_end_page 1382
container_issue 3
container_start_page 1367
container_title Numerical algorithms
container_volume 97
creator Wang, Tao
Li, Ying
Wei, Musheng
Xi, Yimeng
Zhang, Mingcui
description Due to the increasing applications of dual quaternion and their matrices in recent years, as well as the significance of LU decomposition as a matrix decomposition technique, in this paper, we propose dual quaternion Gaussian transformation and obtain dual quaternion LU decomposition by using Gaussian transformation. We also use the total order of dual numbers to obtain the partial pivoting dual quaternion LU decomposition. Based on the real structure-preserving algorithm of quaternion matrix, we propose the real structure-preserving algorithms of LU decomposition and partial pivoting LU decomposition for dual quaternion matrix. Numerical experiments have verified the effectiveness of the new real structure-preserving approaches.
doi_str_mv 10.1007/s11075-024-01753-8
format article
fullrecord <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_journals_3113876924</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>3113876924</sourcerecordid><originalsourceid>FETCH-LOGICAL-c270t-8511bb95c0ef7e478e08a49f07254de43863a8b5bce75ca4ad8b9e76711b6673</originalsourceid><addsrcrecordid>eNp9kE1LxDAQhosouK7-AU8Bz9GkbZr0uCx-wYKX9RzSdNrt0jbdSSr67826gjdPM7y8zww8SXLL2T1nTD54zpkUlKU5ZVyKjKqzZMGFTGmZFuI87jGmPCvVZXLl_Z6xiKVykYRV30KFprNkgLBzNWkcks07qcG6YXK-C50biWtIPZueHGYTAMdjNJiA3ScxY0264Il1iOAnN9bd2BIfcLZhRqBTTAE_jqHpW4dd2A3XyUVjeg83v3OZbJ8et-sXunl7fl2vNtSmkgWqBOdVVQrLoJGQSwVMmbxsmExFXkOeqSIzqhKVBSmsyU2tqhJkISNWFDJbJnensxO6www-6L2bcYwfdcZ5pmRRpnlspaeWRec9QqMn7AaDX5ozfZSrT3J1lKt_5GoVoewE-VgeW8C_0_9Q38EDfzs</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>3113876924</pqid></control><display><type>article</type><title>Algebraic method for LU decomposition of dual quaternion matrix and its corresponding structure-preserving algorithm</title><source>Springer Link</source><creator>Wang, Tao ; Li, Ying ; Wei, Musheng ; Xi, Yimeng ; Zhang, Mingcui</creator><creatorcontrib>Wang, Tao ; Li, Ying ; Wei, Musheng ; Xi, Yimeng ; Zhang, Mingcui</creatorcontrib><description>Due to the increasing applications of dual quaternion and their matrices in recent years, as well as the significance of LU decomposition as a matrix decomposition technique, in this paper, we propose dual quaternion Gaussian transformation and obtain dual quaternion LU decomposition by using Gaussian transformation. We also use the total order of dual numbers to obtain the partial pivoting dual quaternion LU decomposition. Based on the real structure-preserving algorithm of quaternion matrix, we propose the real structure-preserving algorithms of LU decomposition and partial pivoting LU decomposition for dual quaternion matrix. Numerical experiments have verified the effectiveness of the new real structure-preserving approaches.</description><identifier>ISSN: 1017-1398</identifier><identifier>EISSN: 1572-9265</identifier><identifier>DOI: 10.1007/s11075-024-01753-8</identifier><language>eng</language><publisher>New York: Springer US</publisher><subject>Algebra ; Algorithms ; Computer Science ; Coordinate transformations ; Decomposition ; Numbers ; Numeric Computing ; Numerical Analysis ; Original Paper ; Quaternions ; Robots ; Theory of Computation ; Transformations (mathematics)</subject><ispartof>Numerical algorithms, 2024-11, Vol.97 (3), p.1367-1382</ispartof><rights>The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2024. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c270t-8511bb95c0ef7e478e08a49f07254de43863a8b5bce75ca4ad8b9e76711b6673</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,780,784,27924,27925</link.rule.ids></links><search><creatorcontrib>Wang, Tao</creatorcontrib><creatorcontrib>Li, Ying</creatorcontrib><creatorcontrib>Wei, Musheng</creatorcontrib><creatorcontrib>Xi, Yimeng</creatorcontrib><creatorcontrib>Zhang, Mingcui</creatorcontrib><title>Algebraic method for LU decomposition of dual quaternion matrix and its corresponding structure-preserving algorithm</title><title>Numerical algorithms</title><addtitle>Numer Algor</addtitle><description>Due to the increasing applications of dual quaternion and their matrices in recent years, as well as the significance of LU decomposition as a matrix decomposition technique, in this paper, we propose dual quaternion Gaussian transformation and obtain dual quaternion LU decomposition by using Gaussian transformation. We also use the total order of dual numbers to obtain the partial pivoting dual quaternion LU decomposition. Based on the real structure-preserving algorithm of quaternion matrix, we propose the real structure-preserving algorithms of LU decomposition and partial pivoting LU decomposition for dual quaternion matrix. Numerical experiments have verified the effectiveness of the new real structure-preserving approaches.</description><subject>Algebra</subject><subject>Algorithms</subject><subject>Computer Science</subject><subject>Coordinate transformations</subject><subject>Decomposition</subject><subject>Numbers</subject><subject>Numeric Computing</subject><subject>Numerical Analysis</subject><subject>Original Paper</subject><subject>Quaternions</subject><subject>Robots</subject><subject>Theory of Computation</subject><subject>Transformations (mathematics)</subject><issn>1017-1398</issn><issn>1572-9265</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2024</creationdate><recordtype>article</recordtype><recordid>eNp9kE1LxDAQhosouK7-AU8Bz9GkbZr0uCx-wYKX9RzSdNrt0jbdSSr67826gjdPM7y8zww8SXLL2T1nTD54zpkUlKU5ZVyKjKqzZMGFTGmZFuI87jGmPCvVZXLl_Z6xiKVykYRV30KFprNkgLBzNWkcks07qcG6YXK-C50biWtIPZueHGYTAMdjNJiA3ScxY0264Il1iOAnN9bd2BIfcLZhRqBTTAE_jqHpW4dd2A3XyUVjeg83v3OZbJ8et-sXunl7fl2vNtSmkgWqBOdVVQrLoJGQSwVMmbxsmExFXkOeqSIzqhKVBSmsyU2tqhJkISNWFDJbJnensxO6www-6L2bcYwfdcZ5pmRRpnlspaeWRec9QqMn7AaDX5ozfZSrT3J1lKt_5GoVoewE-VgeW8C_0_9Q38EDfzs</recordid><startdate>20241101</startdate><enddate>20241101</enddate><creator>Wang, Tao</creator><creator>Li, Ying</creator><creator>Wei, Musheng</creator><creator>Xi, Yimeng</creator><creator>Zhang, Mingcui</creator><general>Springer US</general><general>Springer Nature B.V</general><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>PRINS</scope><scope>PTHSS</scope></search><sort><creationdate>20241101</creationdate><title>Algebraic method for LU decomposition of dual quaternion matrix and its corresponding structure-preserving algorithm</title><author>Wang, Tao ; Li, Ying ; Wei, Musheng ; Xi, Yimeng ; Zhang, Mingcui</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c270t-8511bb95c0ef7e478e08a49f07254de43863a8b5bce75ca4ad8b9e76711b6673</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2024</creationdate><topic>Algebra</topic><topic>Algorithms</topic><topic>Computer Science</topic><topic>Coordinate transformations</topic><topic>Decomposition</topic><topic>Numbers</topic><topic>Numeric Computing</topic><topic>Numerical Analysis</topic><topic>Original Paper</topic><topic>Quaternions</topic><topic>Robots</topic><topic>Theory of Computation</topic><topic>Transformations (mathematics)</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Wang, Tao</creatorcontrib><creatorcontrib>Li, Ying</creatorcontrib><creatorcontrib>Wei, Musheng</creatorcontrib><creatorcontrib>Xi, Yimeng</creatorcontrib><creatorcontrib>Zhang, Mingcui</creatorcontrib><collection>CrossRef</collection><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>Materials Science &amp; Engineering Collection</collection><collection>ProQuest Central</collection><collection>Advanced Technologies &amp; 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</collection><collection>ProQuest Central Student</collection><collection>SciTech Premium Collection (Proquest) (PQ_SDU_P3)</collection><collection>ProQuest Computer Science Collection</collection><collection>Computer Science Database</collection><collection>ProQuest Engineering Collection</collection><collection>Engineering Database</collection><collection>ProQuest Advanced Technologies &amp; 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>ProQuest Central China</collection><collection>Engineering Collection</collection><jtitle>Numerical algorithms</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Wang, Tao</au><au>Li, Ying</au><au>Wei, Musheng</au><au>Xi, Yimeng</au><au>Zhang, Mingcui</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Algebraic method for LU decomposition of dual quaternion matrix and its corresponding structure-preserving algorithm</atitle><jtitle>Numerical algorithms</jtitle><stitle>Numer Algor</stitle><date>2024-11-01</date><risdate>2024</risdate><volume>97</volume><issue>3</issue><spage>1367</spage><epage>1382</epage><pages>1367-1382</pages><issn>1017-1398</issn><eissn>1572-9265</eissn><abstract>Due to the increasing applications of dual quaternion and their matrices in recent years, as well as the significance of LU decomposition as a matrix decomposition technique, in this paper, we propose dual quaternion Gaussian transformation and obtain dual quaternion LU decomposition by using Gaussian transformation. We also use the total order of dual numbers to obtain the partial pivoting dual quaternion LU decomposition. Based on the real structure-preserving algorithm of quaternion matrix, we propose the real structure-preserving algorithms of LU decomposition and partial pivoting LU decomposition for dual quaternion matrix. Numerical experiments have verified the effectiveness of the new real structure-preserving approaches.</abstract><cop>New York</cop><pub>Springer US</pub><doi>10.1007/s11075-024-01753-8</doi><tpages>16</tpages></addata></record>
fulltext fulltext
identifier ISSN: 1017-1398
ispartof Numerical algorithms, 2024-11, Vol.97 (3), p.1367-1382
issn 1017-1398
1572-9265
language eng
recordid cdi_proquest_journals_3113876924
source Springer Link
subjects Algebra
Algorithms
Computer Science
Coordinate transformations
Decomposition
Numbers
Numeric Computing
Numerical Analysis
Original Paper
Quaternions
Robots
Theory of Computation
Transformations (mathematics)
title Algebraic method for LU decomposition of dual quaternion matrix and its corresponding structure-preserving algorithm
url http://sfxeu10.hosted.exlibrisgroup.com/loughborough?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-07T11%3A33%3A27IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Algebraic%20method%20for%20LU%20decomposition%20of%20dual%20quaternion%20matrix%20and%20its%20corresponding%20structure-preserving%20algorithm&rft.jtitle=Numerical%20algorithms&rft.au=Wang,%20Tao&rft.date=2024-11-01&rft.volume=97&rft.issue=3&rft.spage=1367&rft.epage=1382&rft.pages=1367-1382&rft.issn=1017-1398&rft.eissn=1572-9265&rft_id=info:doi/10.1007/s11075-024-01753-8&rft_dat=%3Cproquest_cross%3E3113876924%3C/proquest_cross%3E%3Cgrp_id%3Ecdi_FETCH-LOGICAL-c270t-8511bb95c0ef7e478e08a49f07254de43863a8b5bce75ca4ad8b9e76711b6673%3C/grp_id%3E%3Coa%3E%3C/oa%3E%3Curl%3E%3C/url%3E&rft_id=info:oai/&rft_pqid=3113876924&rft_id=info:pmid/&rfr_iscdi=true