LEAST SQUARES WITH EQUALITY CONSTRAINTS

The paper exposes a few useful mathematical facts about ordinary least-squares problems where the vector of unknows x is subject to constraints. They are given as a system of equations. Constraints often follow from a mathematical or physical model. In its simplest form certain prescribed coordinate...

Celý popis

Uloženo v:
Podrobná bibliografie
Vydáno v:Geodezija ir kartografija Ročník 28; číslo 1; s. 3 - 6
Hlavní autoři: Borre, Kai, Borre, K
Médium: Journal Article
Jazyk:angličtina
Vydáno: Taylor & Francis Group 01.01.2002
Témata:
adjustment of geodetic networks
least squares
MATLAB code
ISSN:1392-1541
On-line přístup:Získat plný text
Tagy: Přidat tag
Žádné tagy, Buďte první, kdo vytvoří štítek k tomuto záznamu!
Abstract The paper exposes a few useful mathematical facts about ordinary least-squares problems where the vector of unknows x is subject to constraints. They are given as a system of equations. Constraints often follow from a mathematical or physical model. In its simplest form certain prescribed coordinate values shall be left unchanged by the least-squares procedure. By ,,prescribed" we mean that the numerical values have zero variance. A modification of the problem occurs when the variance is close to zero. The concept of soft/hard postulation due to T. Krarup is given. In order to illustrate the use of various formulas the MATLAB code's examples are included that demonstrates the application of the exposed theory.
AbstractList The paper exposes a few useful mathematical facts about ordinary least-squares problems where the vector of unknows x is subject to constraints. They are given as a system of equations. Constraints often follow from a mathematical or physical model. In its simplest form certain prescribed coordinate values shall be left unchanged by the least-squares procedure. By ,,prescribed" we mean that the numerical values have zero variance. A modification of the problem occurs when the variance is close to zero. The concept of soft/hard postulation due to T. Krarup is given. In order to illustrate the use of various formulas the MATLAB code's examples are included that demonstrates the application of the exposed theory.
Author Borre, K
Borre, Kai
Author_xml – sequence: 1
  givenname: Kai
  surname: Borre
  fullname: Borre, Kai
  organization: Danish GPS Center , Aalborg University
– sequence: 2
  givenname: K
  surname: Borre
  fullname: Borre, K
  organization: Danish GPS Center , Aalborg University
BookMark eNo1j81qg0AYRWeRQn7aVyjuujL9vvnRmaWIbQRJaJwQuhpGZwSLVdBA6ds3kmZ1uffAhbMmi37oPSHPCFsECa_IFEXBcUsB6HUSgiomF2Q1g3AmS7Kepi-YCRcr8lJkSamD8uOUHLMyOOd6F2TXUuT6M0gP-1Ifk3yvy0fy0Nhu8k__uSGnt0ynu7A4vOdpUoQtUnkJa28td6xBilxUsRI1KiehsbGLbK2QuxgVQ4_ogVYVAxc5sC6qJQepwLINSW6_bd8M47f9GcbOmYv97YaxGW1ft5NhCGa2NXdbM9uauy37A11PR7Q
ContentType Journal Article
Copyright Copyright Taylor & Francis Group, LLC 2002
Copyright_xml – notice: Copyright Taylor & Francis Group, LLC 2002
DOI 10.1080/13921541.2002.10552938
DatabaseTitleList
DeliveryMethod fulltext_linktorsrc
Discipline Engineering
EndPage 6
ExternalDocumentID 10552938
GroupedDBID .QJ
5GY
AAGME
ABCCY
ABFIM
ABPEM
ACDHJ
ACZPZ
ADCVX
ADOPC
AGMYJ
AIJEM
ALMA_UNASSIGNED_HOLDINGS
AQTUD
AVBZW
BFWEY
CS3
CWRZV
ESX
E~A
E~B
H13
IAO
IEA
JEPSP
M4Z
P2P
PCLFJ
S-T
TDBHL
TEI
TFL
TFW
TUS
UT5
UU3
~02
~S~
ID FETCH-LOGICAL-i128t-ceaa4d3f12145b795c19d80fa7d6ac914d71931e11e02bb30d6d0ad6c840890a3
IEDL.DBID TFW
ISSN 1392-1541
IngestDate Mon Oct 20 23:43:52 EDT 2025
IsPeerReviewed false
IsScholarly false
Issue 1
Language English
LinkModel DirectLink
MergedId FETCHMERGED-LOGICAL-i128t-ceaa4d3f12145b795c19d80fa7d6ac914d71931e11e02bb30d6d0ad6c840890a3
PageCount 4
ParticipantIDs informaworld_taylorfrancis_310_1080_13921541_2002_10552938
PublicationCentury 2000
PublicationDate 1/1/2002
PublicationDateYYYYMMDD 2002-01-01
PublicationDate_xml – month: 01
  year: 2002
  text: 1/1/2002
  day: 01
PublicationDecade 2000
PublicationTitle Geodezija ir kartografija
PublicationYear 2002
Publisher Taylor & Francis Group
Publisher_xml – name: Taylor & Francis Group
SSID ssj0055245
Score 1.300372
Snippet The paper exposes a few useful mathematical facts about ordinary least-squares problems where the vector of unknows x is subject to constraints. They are given...
SourceID informaworld
SourceType Publisher
StartPage 3
SubjectTerms adjustment of geodetic networks
least squares
MATLAB code
Title LEAST SQUARES WITH EQUALITY CONSTRAINTS
URI https://www.tandfonline.com/doi/abs/10.1080/13921541.2002.10552938
Volume 28
hasFullText 1
inHoldings 1
isFullTextHit
isPrint
journalDatabaseRights – providerCode: PRVAWR
  databaseName: Taylor & Francis Journals Complete
  issn: 1392-1541
  databaseCode: TFW
  dateStart: 19950101
  customDbUrl:
  isFulltext: true
  dateEnd: 20100131
  titleUrlDefault: https://www.tandfonline.com
  omitProxy: false
  ssIdentifier: ssj0055245
  providerName: Taylor & Francis
link http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwrV09a8MwED1K6NAO_S79xkOhk6hkO7bVLQSHBII72CXpFGSdDFlcSNz-_p7kGEyhUzsac8KcT_fuhO49gEccailMgsxQ68Uo4SGToY_U80gKp6H0E45ObCLOsmS5lP1ZGHut0vbQVUsU4XK13dyq3HY34p6paCGgCl1351uhWruwnfcl7Ld7s5gsumRMr5xOsTVh1qYbEv51mR-UpT2wmRz_x2eewNGu1PRGbWycwp6pz-CwR0B4Dk_zdJQXXm7r2jT3FrNi6qX0MJ8V7974NbOKyrOsyC_gbZIW4ynbSSewNQFOw7RRKsSgEpaIvIzlUAuJCa9UjJGivxNiTJWbMEIY7pdlwDFCrjDS1O8lkqvgEgb1R22uwKskGSjjS5UQ-uuIChytopIwTVUCOV7DS99hq8adNFStLMgqEDsO0s4bVvfSX3XeuPmL8S0cOG0WdyByB4Nm82nuYV9_Nevt5sHFwTdSvaty
linkProvider Taylor & Francis
linkToHtml http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwrV1LS8QwEB7WVVAPvsW3PQieikmfibdl6bLFWoVGVk8lbVLYywpr9fc7yW5hETzpsZQJZTqZ-WZIvg_gRoU1p5opV2Pr5WLCUy4PPIU9D8dwCrnHiLJiE3Ges9dX_tyDYXcXxhyrND10syCKsLnabG4zjO6OxN0hasFKFdj2zjNKtWZltgbrIRZbQ6AvRpMuHeM7q1RsbFxj1F0T_nWdH6SlK-VmtPsvH7oHO0u06QwW4bEPPT07gO0VDsJDuM2SQSGcwkDbpHAmqRg7CT5kqXhzhk-5EVVOc1EcwcsoEcOxu1RPcKdYc1q31lIGym-o4SKvYh7WlCtGGhmrSOIPClSM4I1qSjXxqsonKlJEqqjGlo9xIv1j6M_eZ_oEnIajgdQelwwBQB0hxqllVGFZkw1VRJ3C_arHytYOG5qFMkjp0yUNaecNI33plZ03zv5ifA2bY_GYlVmaP5zDlpVqsfORC-i38099CRv1Vzv9mF_ZoPgGZaOvnA
linkToPdf http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwrV1NS8QwEB10FdGD3-K3PQieik3bbRNvi7ZscalCK7ueStpJYS-rrNXf7yS7hSJ40mMJE8J0MvMmJO8BXGO_EkxxtBW1XjYlPLSF7yL1PILCqS9c7qARmwjTlE8movsWRl-r1D10vSCKMLlab-53rNsbcbcEWqhQ-aa7c7VQrZ6Yr8IaYedAR3kej9tsTGNGqFjb2NqofSX86zw_OEs71Sbe-Y917sL2Emtag0Vw7MGKmu3DVoeB8ABuRtEgy61MA9sos8ZJPrQi-hgl-at1_5RqSeUkzbNDeImj_H5oL7UT7ClVnMaulJQ-ejXTTORlKPoVE8idWoYYSPo9PoYE3ZhiTDluWXoOBuhIDCpq-LhwpHcEvdnbTB2DVQsykMoVklP5rwJCOJUMSipqsmbo4AncdR1WNOaooV7oghQeW5KQtt7Qwpdu0Xrj9C_GV7Dx_BAXoyR9PINNo9NiDkfOodfMP9UFrFdfzfRjfmlC4huFQq5O
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=LEAST+SQUARES+WITH+EQUALITY+CONSTRAINTS&rft.jtitle=Geodezija+ir+kartografija&rft.au=Borre%2C+Kai&rft.au=Borre%2C+K&rft.date=2002-01-01&rft.pub=Taylor+%26+Francis+Group&rft.issn=1392-1541&rft.volume=28&rft.issue=1&rft.spage=3&rft.epage=6&rft_id=info:doi/10.1080%2F13921541.2002.10552938&rft.externalDocID=10552938
thumbnail_l http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=1392-1541&client=summon
thumbnail_m http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=1392-1541&client=summon
thumbnail_s http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=1392-1541&client=summon