CMMSE algorithms for constructing doubly stochastic matrices with the relative gain array (combined matrix) A circle A(-T)

[EN] The Combined matrix of a nonsingular matrix A is defined by phi(A)=A T where degrees means the Hadamard (entrywise) product. If the matrix A describes the relation between inputs and outputs in a multivariable process control, phi(A) describes the relative gain array (RGA) of the process and it...

Full description

Bibliographic Details
Authors: Fuster Capilla, Robert Ricard, Gasso Matoses, María Teresa, Gimenez Manglano, María Isabel
Format: article
Publication Date:2019
Country:España
Institution:Universitat Politècnica de València (UPV)
Repository:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
Language:English
OAI Identifier:oai:riunet.upv.es:10251/158844
Online Access:https://riunet.upv.es/handle/10251/158844
Access Level:Open access
Keyword:Hadamard product
Combined matrix
Doubly stochastic matrix
Hessenberg matrix
Householder matrix
Orthogonal matrix
Unitary matrix
Relative gain array
MATEMATICA APLICADA
id ES_b8481cd6c4c3bb55674f8b2ecfadbc1a
oai_identifier_str oai:riunet.upv.es:10251/158844
network_acronym_str ES
network_name_str España
repository_id_str
spelling CMMSE algorithms for constructing doubly stochastic matrices with the relative gain array (combined matrix) A circle A(-T)Fuster Capilla, Robert RicardGasso Matoses, María TeresaGimenez Manglano, María IsabelHadamard productCombined matrixDoubly stochastic matrixHessenberg matrixHouseholder matrixOrthogonal matrixUnitary matrixRelative gain arrayMATEMATICA APLICADA[EN] The Combined matrix of a nonsingular matrix A is defined by phi(A)=A T where degrees means the Hadamard (entrywise) product. If the matrix A describes the relation between inputs and outputs in a multivariable process control, phi(A) describes the relative gain array (RGA) of the process and it defines the Bristol method (IEEE Trans Autom Control 1:133-134, 1966) often used for Chemical processes (McAvoy in Interaction analysis: principles and applications. Instrument Society of America, Pittsburgh, 1983; Papadourakis et al. in Ind Eng Chem Res 26(6):1259-1262, 1987; Wang et al. in Chem Eng Technol, 10.1002/ceat.201500202, 2016; Kariwala et al. in Ind Eng Chem Res 45(5):1751-1757, 10.1021/ie050790r, 2006; Golender et al. in J Chem Inf Comput Sci 21(4):196-204, 10.1021/ci00032a004, 1981). The combined matrix has been studied in several works such as Bru et al. (J Appl Math, 10.1155/2014/182354, 2014), Fiedler and Markham (Linear Algebra Appl 435:1945-1955, 2011) and Johnson and Shapiro (SIAM J Algebraic Discrete Methods 7:627-644, 1986). Since phi(A)=(cij) has the property of Sigma kcik=Sigma kckj=1,i,j, when phi(A)>= 0, phi(A) is a doubly stochastic matrix. In certain chemical engineering applications a diagonal of the RGA in wchich the entries are near 1 is used to determine the pairing of inputs and outputs for further design analysis. Applications of these matrices can be found in Communication Theory, related with the satellite-switched time division multiple-access systems, and about a doubly stochastic automorphism of a graph. In this paper we present new algorithms to generate doubly stochastic matrices with the Combined matrix using Hessenberg matrices in Sect.3 and orthogonal/unitary matrices in Sect.4. In addition, we discuss what kind of doubly stochastic matrices are obtained with our algorithms and the possibility of generating a particular doubly stochastic matrix by the map phi.This work has been supported by Spanish Ministerio de Economia y Competitividad Grants MTM2014-58159-P, MTM2017-85669-P and MTM2017-90682-REDT.Springer-VerlagAgencia Estatal de InvestigaciónMinisterio de Economía y CompetitividadRepositorio Institucional de la Universitat Politècnica de València Riunet20192019-08-01journal articlehttp://purl.org/coar/resource_type/c_6501VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/articleapplication/pdfapplication/pdfhttps://riunet.upv.es/handle/10251/158844reponame:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valénciainstname:Universitat Politècnica de València (UPV)InglésengAgencia Estatal de Investigación http://dx.doi.org/10.13039/501100011033 MTM2017-90682-REDT RED TEMATICA DE ALGEBRA LINEAL, ANALISIS MATRICIAL Y APLICACIONESMinisterio de Economía y Competitividad http://dx.doi.org/10.13039/501100003329 MTM2014-58159-P PRECONDICIONADORES PARA SISTEMAS DE ECUACIONES LINEALES, PROBLEMAS DE MINIMOS CUADRADOS, CALCULO DE VALORES PROPIOS Y APLICACIONES TECNOLOGICASAgencia Estatal de Investigación http://dx.doi.org/10.13039/501100011033 Plan Estatal de Investigación Científica y Técnica y de Innovación 2013-2016 MTM2017-85669-P PROBLEMAS MATRICIALES: COMPUTACION, TEORIA Y APLICACIONESopen accesshttp://purl.org/coar/access_right/c_abf2Reserva de todos los derechoshttp://rightsstatements.org/vocab/InC/1.0/info:eu-repo/semantics/openAccessoai:riunet.upv.es:10251/1588442026-06-13T07:49:27Z
dc.title.none.fl_str_mv CMMSE algorithms for constructing doubly stochastic matrices with the relative gain array (combined matrix) A circle A(-T)
title CMMSE algorithms for constructing doubly stochastic matrices with the relative gain array (combined matrix) A circle A(-T)
spellingShingle CMMSE algorithms for constructing doubly stochastic matrices with the relative gain array (combined matrix) A circle A(-T)
Fuster Capilla, Robert Ricard
Hadamard product
Combined matrix
Doubly stochastic matrix
Hessenberg matrix
Householder matrix
Orthogonal matrix
Unitary matrix
Relative gain array
MATEMATICA APLICADA
title_short CMMSE algorithms for constructing doubly stochastic matrices with the relative gain array (combined matrix) A circle A(-T)
title_full CMMSE algorithms for constructing doubly stochastic matrices with the relative gain array (combined matrix) A circle A(-T)
title_fullStr CMMSE algorithms for constructing doubly stochastic matrices with the relative gain array (combined matrix) A circle A(-T)
title_full_unstemmed CMMSE algorithms for constructing doubly stochastic matrices with the relative gain array (combined matrix) A circle A(-T)
title_sort CMMSE algorithms for constructing doubly stochastic matrices with the relative gain array (combined matrix) A circle A(-T)
dc.creator.none.fl_str_mv Fuster Capilla, Robert Ricard
Gasso Matoses, María Teresa
Gimenez Manglano, María Isabel
author Fuster Capilla, Robert Ricard
author_facet Fuster Capilla, Robert Ricard
Gasso Matoses, María Teresa
Gimenez Manglano, María Isabel
author_role author
author2 Gasso Matoses, María Teresa
Gimenez Manglano, María Isabel
author2_role author
author
dc.contributor.none.fl_str_mv Agencia Estatal de Investigación
Ministerio de Economía y Competitividad
Repositorio Institucional de la Universitat Politècnica de València Riunet
dc.subject.none.fl_str_mv Hadamard product
Combined matrix
Doubly stochastic matrix
Hessenberg matrix
Householder matrix
Orthogonal matrix
Unitary matrix
Relative gain array
MATEMATICA APLICADA
topic Hadamard product
Combined matrix
Doubly stochastic matrix
Hessenberg matrix
Householder matrix
Orthogonal matrix
Unitary matrix
Relative gain array
MATEMATICA APLICADA
description [EN] The Combined matrix of a nonsingular matrix A is defined by phi(A)=A T where degrees means the Hadamard (entrywise) product. If the matrix A describes the relation between inputs and outputs in a multivariable process control, phi(A) describes the relative gain array (RGA) of the process and it defines the Bristol method (IEEE Trans Autom Control 1:133-134, 1966) often used for Chemical processes (McAvoy in Interaction analysis: principles and applications. Instrument Society of America, Pittsburgh, 1983; Papadourakis et al. in Ind Eng Chem Res 26(6):1259-1262, 1987; Wang et al. in Chem Eng Technol, 10.1002/ceat.201500202, 2016; Kariwala et al. in Ind Eng Chem Res 45(5):1751-1757, 10.1021/ie050790r, 2006; Golender et al. in J Chem Inf Comput Sci 21(4):196-204, 10.1021/ci00032a004, 1981). The combined matrix has been studied in several works such as Bru et al. (J Appl Math, 10.1155/2014/182354, 2014), Fiedler and Markham (Linear Algebra Appl 435:1945-1955, 2011) and Johnson and Shapiro (SIAM J Algebraic Discrete Methods 7:627-644, 1986). Since phi(A)=(cij) has the property of Sigma kcik=Sigma kckj=1,i,j, when phi(A)>= 0, phi(A) is a doubly stochastic matrix. In certain chemical engineering applications a diagonal of the RGA in wchich the entries are near 1 is used to determine the pairing of inputs and outputs for further design analysis. Applications of these matrices can be found in Communication Theory, related with the satellite-switched time division multiple-access systems, and about a doubly stochastic automorphism of a graph. In this paper we present new algorithms to generate doubly stochastic matrices with the Combined matrix using Hessenberg matrices in Sect.3 and orthogonal/unitary matrices in Sect.4. In addition, we discuss what kind of doubly stochastic matrices are obtained with our algorithms and the possibility of generating a particular doubly stochastic matrix by the map phi.
publishDate 2019
dc.date.none.fl_str_mv 2019
2019-08-01
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
VoR
http://purl.org/coar/version/c_970fb48d4fbd8a85
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://riunet.upv.es/handle/10251/158844
url https://riunet.upv.es/handle/10251/158844
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.relation.none.fl_str_mv Agencia Estatal de Investigación http://dx.doi.org/10.13039/501100011033 MTM2017-90682-REDT RED TEMATICA DE ALGEBRA LINEAL, ANALISIS MATRICIAL Y APLICACIONES
Ministerio de Economía y Competitividad http://dx.doi.org/10.13039/501100003329 MTM2014-58159-P PRECONDICIONADORES PARA SISTEMAS DE ECUACIONES LINEALES, PROBLEMAS DE MINIMOS CUADRADOS, CALCULO DE VALORES PROPIOS Y APLICACIONES TECNOLOGICAS
Agencia Estatal de Investigación http://dx.doi.org/10.13039/501100011033 Plan Estatal de Investigación Científica y Técnica y de Innovación 2013-2016 MTM2017-85669-P PROBLEMAS MATRICIALES: COMPUTACION, TEORIA Y APLICACIONES
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
Reserva de todos los derechos
http://rightsstatements.org/vocab/InC/1.0/
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
Reserva de todos los derechos
http://rightsstatements.org/vocab/InC/1.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Springer-Verlag
publisher.none.fl_str_mv Springer-Verlag
dc.source.none.fl_str_mv reponame:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
instname:Universitat Politècnica de València (UPV)
instname_str Universitat Politècnica de València (UPV)
reponame_str RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
collection RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
repository.name.fl_str_mv
repository.mail.fl_str_mv
_version_ 1869417617528193024
score 15,301603

Similar Items