Iterative methods to solve the constrained Sylvester equation

In this paper, the multiple constraint least squares solution of the Sylvester equation $ AX+XB = C $ is discussed. The necessary and sufficient conditions for the existence of solutions to the considered matrix equation are given. Noting that the alternating direction method of multipliers (ADMM) i...

Full description

Saved in:
Bibliographic Details
Published inAIMS mathematics Vol. 8; no. 9; pp. 21531 - 21553
Main Authors Yu, Siting, Peng, Jingjing, Tang, Zengao, Peng, Zhenyun
Format Journal Article
LanguageEnglish
Published AIMS Press 01.01.2023
Subjects
anderson acceleration algorithm
fixed point iteration algorithm
nonlinear matrix equation
thompson distance
Online AccessGet full text
ISSN2473-6988
2473-6988
DOI10.3934/math.20231097

Cover

Abstract In this paper, the multiple constraint least squares solution of the Sylvester equation $ AX+XB = C $ is discussed. The necessary and sufficient conditions for the existence of solutions to the considered matrix equation are given. Noting that the alternating direction method of multipliers (ADMM) is a one-step iterative method, a multi-step alternating direction method of multipliers (MSADMM) to solve the considered matrix equation is proposed and some convergence results of the proposed algorithm are proved. Problems that should be studied in the near future are listed. Numerical comparisons between MSADMM, ADMM and ADMM with Anderson acceleration (ACADMM) are included.
AbstractList In this paper, the multiple constraint least squares solution of the Sylvester equation $ AX+XB = C $ is discussed. The necessary and sufficient conditions for the existence of solutions to the considered matrix equation are given. Noting that the alternating direction method of multipliers (ADMM) is a one-step iterative method, a multi-step alternating direction method of multipliers (MSADMM) to solve the considered matrix equation is proposed and some convergence results of the proposed algorithm are proved. Problems that should be studied in the near future are listed. Numerical comparisons between MSADMM, ADMM and ADMM with Anderson acceleration (ACADMM) are included.
Author Peng, Jingjing
Yu, Siting
Tang, Zengao
Peng, Zhenyun
Author_xml – sequence: 1
  givenname: Siting
  surname: Yu
  fullname: Yu, Siting
– sequence: 2
  givenname: Jingjing
  surname: Peng
  fullname: Peng, Jingjing
– sequence: 3
  givenname: Zengao
  surname: Tang
  fullname: Tang, Zengao
– sequence: 4
  givenname: Zhenyun
  surname: Peng
  fullname: Peng, Zhenyun
BookMark eNptkM1LAzEQxYNUsGqP3vcf2Dr5aJI9eJDiR6HgQT2HJDtrt2w3mkSh_73b1oKIpxke837Me-dk1IceCbmiMOUVF9cbm1dTBoxTqNQJGTOheCkrrUe_9jMySWkNAIwywZQYk5tFxmhz-4XFBvMq1KnIoUihG4S8wsKHPuVo2x7r4nk7qGm4L_Djc_CE_pKcNrZLOPmZF-T1_u5l_lgunx4W89tl6bmmuZScaaFrDUp6Rq0TYC1VvBJi1ugGHHDmULlKOMqlRGml143zVDLHa4nAL8jiwK2DXZv32G5s3JpgW7MXQnwzNubWd2jASSkFZzMFAw-ddlA3DZNOKi_Qi4HFDywfQ0oRG-PbvE-zy9kZCmZXqNkVao6FDq7yj-v4xf_3387Bedw
CitedBy_id crossref_primary_10_3390_math13020318
crossref_primary_10_3390_math12121901
Cites_doi 10.1007/s10915-015-0150-0
10.1016/0167-7152(91)90006-D
10.1016/S0096-3003(02)00478-2
10.1109/9.57015
10.1137/0116017
10.1145/361573.361582
10.1137/S0895479894273687
10.1016/j.laa.2020.08.009
10.1145/355780.355784
10.1137/10078356X
10.1080/00207160802516875
10.1016/S0024-3795(02)00283-5
10.1137/0729049
10.1109/TAC.1979.1102170
10.1145/321296.321305
10.1137/070711578
10.1080/00207178008922881
10.1134/S0040577923030042
10.1007/978-3-0348-8328-3
10.1137/1.9780898718713
10.1002/nla.605
10.1016/j.camwa.2007.04.048
10.1112/S0024609396001828
10.1007/BF01581204
10.1002/nla.617
10.1007/s11075-015-0078-3
10.1080/00207179108953642
ContentType Journal Article
DBID AAYXX
CITATION
DOA
DOI 10.3934/math.20231097
DatabaseName CrossRef
DOAJ Directory of Open Access Journals
DatabaseTitle CrossRef
DatabaseTitleList CrossRef
Database_xml – sequence: 1
  dbid: DOA
  name: DOAJ Directory of Open Access Journals
  url: https://www.doaj.org/
  sourceTypes: Open Website
DeliveryMethod fulltext_linktorsrc
Discipline Mathematics
EISSN 2473-6988
EndPage 21553
ExternalDocumentID oai_doaj_org_article_0b66643257094beb8b0dff26b67c4ec4
10_3934_math_20231097
GroupedDBID AAYXX
ADBBV
ALMA_UNASSIGNED_HOLDINGS
AMVHM
BCNDV
CITATION
EBS
FRJ
GROUPED_DOAJ
IAO
ITC
M~E
OK1
RAN
ID FETCH-LOGICAL-c381t-632848d8076c21ab40aa1739445f8f0b032be7b94b1366e6a6c8fbc162b3d6e03
IEDL.DBID DOA
ISSN 2473-6988
IngestDate Wed Aug 27 01:14:32 EDT 2025
Thu Apr 24 23:04:43 EDT 2025
Tue Jul 01 03:57:04 EDT 2025
IsDoiOpenAccess true
IsOpenAccess true
IsPeerReviewed true
IsScholarly true
Issue 9
Language English
LinkModel DirectLink
MergedId FETCHMERGED-LOGICAL-c381t-632848d8076c21ab40aa1739445f8f0b032be7b94b1366e6a6c8fbc162b3d6e03
OpenAccessLink https://doaj.org/article/0b66643257094beb8b0dff26b67c4ec4
PageCount 23
ParticipantIDs doaj_primary_oai_doaj_org_article_0b66643257094beb8b0dff26b67c4ec4
crossref_citationtrail_10_3934_math_20231097
crossref_primary_10_3934_math_20231097
ProviderPackageCode CITATION
AAYXX
PublicationCentury 2000
PublicationDate 2023-01-01
PublicationDateYYYYMMDD 2023-01-01
PublicationDate_xml – month: 01
  year: 2023
  text: 2023-01-01
  day: 01
PublicationDecade 2020
PublicationTitle AIMS mathematics
PublicationYear 2023
Publisher AIMS Press
Publisher_xml – name: AIMS Press
References key-10.3934/math.20231097-29
key-10.3934/math.20231097-28
key-10.3934/math.20231097-2
key-10.3934/math.20231097-21
key-10.3934/math.20231097-3
key-10.3934/math.20231097-20
key-10.3934/math.20231097-4
key-10.3934/math.20231097-23
key-10.3934/math.20231097-5
key-10.3934/math.20231097-22
key-10.3934/math.20231097-6
key-10.3934/math.20231097-25
key-10.3934/math.20231097-7
key-10.3934/math.20231097-24
key-10.3934/math.20231097-8
key-10.3934/math.20231097-27
key-10.3934/math.20231097-9
key-10.3934/math.20231097-26
key-10.3934/math.20231097-18
key-10.3934/math.20231097-17
key-10.3934/math.20231097-19
key-10.3934/math.20231097-10
key-10.3934/math.20231097-32
key-10.3934/math.20231097-31
key-10.3934/math.20231097-12
key-10.3934/math.20231097-34
key-10.3934/math.20231097-11
key-10.3934/math.20231097-33
key-10.3934/math.20231097-14
key-10.3934/math.20231097-36
key-10.3934/math.20231097-13
key-10.3934/math.20231097-35
key-10.3934/math.20231097-16
key-10.3934/math.20231097-38
key-10.3934/math.20231097-15
key-10.3934/math.20231097-37
key-10.3934/math.20231097-30
key-10.3934/math.20231097-1
References_xml – ident: key-10.3934/math.20231097-31
  doi: 10.1007/s10915-015-0150-0
– ident: key-10.3934/math.20231097-29
  doi: 10.1016/0167-7152(91)90006-D
– ident: key-10.3934/math.20231097-30
  doi: 10.1016/S0096-3003(02)00478-2
– ident: key-10.3934/math.20231097-12
  doi: 10.1109/9.57015
– ident: key-10.3934/math.20231097-18
  doi: 10.1137/0116017
– ident: key-10.3934/math.20231097-15
  doi: 10.1145/361573.361582
– ident: key-10.3934/math.20231097-19
  doi: 10.1137/S0895479894273687
– ident: key-10.3934/math.20231097-11
  doi: 10.1016/j.laa.2020.08.009
– ident: key-10.3934/math.20231097-2
– ident: key-10.3934/math.20231097-25
– ident: key-10.3934/math.20231097-4
– ident: key-10.3934/math.20231097-23
– ident: key-10.3934/math.20231097-14
  doi: 10.1145/355780.355784
– ident: key-10.3934/math.20231097-27
– ident: key-10.3934/math.20231097-37
  doi: 10.1137/10078356X
– ident: key-10.3934/math.20231097-34
  doi: 10.1080/00207160802516875
– ident: key-10.3934/math.20231097-9
  doi: 10.1016/S0024-3795(02)00283-5
– ident: key-10.3934/math.20231097-13
  doi: 10.1137/0729049
– ident: key-10.3934/math.20231097-16
  doi: 10.1109/TAC.1979.1102170
– ident: key-10.3934/math.20231097-35
  doi: 10.1145/321296.321305
– ident: key-10.3934/math.20231097-8
  doi: 10.1137/070711578
– ident: key-10.3934/math.20231097-17
  doi: 10.1080/00207178008922881
– ident: key-10.3934/math.20231097-10
  doi: 10.1134/S0040577923030042
– ident: key-10.3934/math.20231097-5
  doi: 10.1007/978-3-0348-8328-3
– ident: key-10.3934/math.20231097-7
  doi: 10.1137/1.9780898718713
– ident: key-10.3934/math.20231097-32
– ident: key-10.3934/math.20231097-24
  doi: 10.1002/nla.605
– ident: key-10.3934/math.20231097-21
  doi: 10.1016/j.camwa.2007.04.048
– ident: key-10.3934/math.20231097-1
  doi: 10.1112/S0024609396001828
– ident: key-10.3934/math.20231097-33
  doi: 10.1007/BF01581204
– ident: key-10.3934/math.20231097-20
– ident: key-10.3934/math.20231097-36
  doi: 10.1002/nla.617
– ident: key-10.3934/math.20231097-22
– ident: key-10.3934/math.20231097-38
  doi: 10.1007/s11075-015-0078-3
– ident: key-10.3934/math.20231097-3
– ident: key-10.3934/math.20231097-26
– ident: key-10.3934/math.20231097-28
– ident: key-10.3934/math.20231097-6
  doi: 10.1080/00207179108953642
SSID ssj0002124274
Score 2.224497
Snippet In this paper, the multiple constraint least squares solution of the Sylvester equation $ AX+XB = C $ is discussed. The necessary and sufficient conditions for...
SourceID doaj
crossref
SourceType Open Website
Enrichment Source
Index Database
StartPage 21531
SubjectTerms anderson acceleration algorithm
fixed point iteration algorithm
nonlinear matrix equation
thompson distance
Title Iterative methods to solve the constrained Sylvester equation
URI https://doaj.org/article/0b66643257094beb8b0dff26b67c4ec4
Volume 8
hasFullText 1
inHoldings 1
isFullTextHit
isPrint
link http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwrV1LSwMxEA7iSQ_iE-uLHMSTS7N578GDiqUK9aKF3pYkmz2VVu0q-O-d2WxLL-LFaxjC8E2Y-SbZ_YaQS8djbWsuMwfBz6RnKiuiMplTSnFpfVFEvNAfPevhWD5N1GRt1Bd-E5bkgRNwfeaBYEuBw9YK6aO3nlV1zbXXJsgYWiVQVrC1ZgpzMCRkCf1WEtUUhZB94H_49oB0BgWe1orQmlZ_W1QGu2SnY4P0NnmxRzbibJ9sj1ZSqosDcvPY6h5DUqJp2vOCNnMKJwYWwIwGJHg45yFW9OV7-tUqH9D4niS8D8l48PB6P8y6mQdZgNrZZFpAvbCVZUYHnjsvmXO5wb9XFWDKPBPcR-MBilxoHbXTwdY-5Jp7UenIxBHZnM1n8ZhQ2AcH3BbBGCtdrm2uKmlCHnntgJXUPXK9BKEMnSA4-jstoTFAzErErFxi1iNXK_O3pITxm-EdIroyQgHrdgHCWnZhLf8K68l_bHJKttCpdGNyRjabj894Dhyi8RftcfkBKVfDiw
linkProvider Directory of Open Access Journals
openUrl ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Iterative+methods+to+solve+the+constrained+Sylvester+equation&rft.jtitle=AIMS+mathematics&rft.au=Yu%2C+Siting&rft.au=Peng%2C+Jingjing&rft.au=Tang%2C+Zengao&rft.au=Peng%2C+Zhenyun&rft.date=2023-01-01&rft.issn=2473-6988&rft.eissn=2473-6988&rft.volume=8&rft.issue=9&rft.spage=21531&rft.epage=21553&rft_id=info:doi/10.3934%2Fmath.20231097&rft.externalDBID=n%2Fa&rft.externalDocID=10_3934_math_20231097
thumbnail_l http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=2473-6988&client=summon
thumbnail_m http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=2473-6988&client=summon
thumbnail_s http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=2473-6988&client=summon