POLYNOMIAL ALGORITHM FOR QUADRATIC FORMS CLASSIFICATION USING GAUSSIAN ELIMINATION

Bibliographic Details
Main Author: Alves, Jesmmer da Silveira; Instituto Federal Goiano - Campus Morrinhos
Publication Date: 2021
Other Authors: Castonguay, Diane; Universidade Federal de Goiás
Language: eng
Source: Revista de Sistemas e Computação
Download full: https://revistas.unifacs.br/index.php/rsc/article/view/7391
Summary: Existing methods for quadratic forms classification have exponential time complexity or use approximation that weaken the result reliability. We develop an algorithm that improves the best case of quadratic form classification in constant time and is polynomial in the worst case. In addition, new strategies were used to guarantee the results reliability, by representing rational numbers as a fraction of integers and to identify linear combinations that are linearly independent using Gaussian Elimination.DOI: 10.36558/rsc.v11i3.7391
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spelling POLYNOMIAL ALGORITHM FOR QUADRATIC FORMS CLASSIFICATION USING GAUSSIAN ELIMINATIONQuadratic forms; Eigen problems; Gaussian Elimination; Algorithm complexityExisting methods for quadratic forms classification have exponential time complexity or use approximation that weaken the result reliability. We develop an algorithm that improves the best case of quadratic form classification in constant time and is polynomial in the worst case. In addition, new strategies were used to guarantee the results reliability, by representing rational numbers as a fraction of integers and to identify linear combinations that are linearly independent using Gaussian Elimination.DOI: 10.36558/rsc.v11i3.7391Revista de Sistemas e Computação - RSCRevistade Sistemas y ComputaciónAlves, Jesmmer da Silveira; Instituto Federal Goiano - Campus MorrinhosCastonguay, Diane; Universidade Federal de Goiás2021-12-02Artigo Avaliado pelos Paresinfo:eu-repo/semantics/publishedVersionapplication/pdfhttps://revistas.unifacs.br/index.php/rsc/article/view/739110.36558/rsc.v11i3.7391Revista de Sistemas e Computação - RSC; v. 11, n. 3 (2021)Revistade Sistemas y Computación; v. 11, n. 3 (2021)reponame:Revista de Sistemas e Computaçãoinstname:Universidade Salvador (UNIFACS)instacron:UNIFACShttps://revistas.unifacs.br/index.php/rsc/article/downloadSuppFile/7391/29255enginfo:eu-repo/semantics/openAccess2021-12-07T18:09:23Zoai:ojs.200.223.74.126:article/7391Revistahttps://revistas.unifacs.br/index.php/rscPRIhttps://revistas.unifacs.br/index.php/rsc/oaipaulo.caetano@unifacs.br || unifacs@nexodoc.com.br2237-29032237-2903opendoar:2021-12-07T18:09:23Revista de Sistemas e Computação - Universidade Salvador (UNIFACS)false
dc.title.none.fl_str_mv POLYNOMIAL ALGORITHM FOR QUADRATIC FORMS CLASSIFICATION USING GAUSSIAN ELIMINATION
title POLYNOMIAL ALGORITHM FOR QUADRATIC FORMS CLASSIFICATION USING GAUSSIAN ELIMINATION
spellingShingle POLYNOMIAL ALGORITHM FOR QUADRATIC FORMS CLASSIFICATION USING GAUSSIAN ELIMINATION
Alves, Jesmmer da Silveira; Instituto Federal Goiano - Campus Morrinhos
Quadratic forms; Eigen problems; Gaussian Elimination; Algorithm complexity
title_short POLYNOMIAL ALGORITHM FOR QUADRATIC FORMS CLASSIFICATION USING GAUSSIAN ELIMINATION
title_full POLYNOMIAL ALGORITHM FOR QUADRATIC FORMS CLASSIFICATION USING GAUSSIAN ELIMINATION
title_fullStr POLYNOMIAL ALGORITHM FOR QUADRATIC FORMS CLASSIFICATION USING GAUSSIAN ELIMINATION
title_full_unstemmed POLYNOMIAL ALGORITHM FOR QUADRATIC FORMS CLASSIFICATION USING GAUSSIAN ELIMINATION
title_sort POLYNOMIAL ALGORITHM FOR QUADRATIC FORMS CLASSIFICATION USING GAUSSIAN ELIMINATION
author Alves, Jesmmer da Silveira; Instituto Federal Goiano - Campus Morrinhos
author_facet Alves, Jesmmer da Silveira; Instituto Federal Goiano - Campus Morrinhos
Castonguay, Diane; Universidade Federal de Goiás
author_role author
author2 Castonguay, Diane; Universidade Federal de Goiás
author2_role author
dc.contributor.none.fl_str_mv
dc.contributor.author.fl_str_mv Alves, Jesmmer da Silveira; Instituto Federal Goiano - Campus Morrinhos
Castonguay, Diane; Universidade Federal de Goiás
dc.subject.por.fl_str_mv Quadratic forms; Eigen problems; Gaussian Elimination; Algorithm complexity
topic Quadratic forms; Eigen problems; Gaussian Elimination; Algorithm complexity
description Existing methods for quadratic forms classification have exponential time complexity or use approximation that weaken the result reliability. We develop an algorithm that improves the best case of quadratic form classification in constant time and is polynomial in the worst case. In addition, new strategies were used to guarantee the results reliability, by representing rational numbers as a fraction of integers and to identify linear combinations that are linearly independent using Gaussian Elimination.DOI: 10.36558/rsc.v11i3.7391
publishDate 2021
dc.date.none.fl_str_mv 2021-12-02
dc.type.driver.fl_str_mv Artigo Avaliado pelos Pares
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
status_str publishedVersion
dc.identifier.uri.fl_str_mv https://revistas.unifacs.br/index.php/rsc/article/view/7391
10.36558/rsc.v11i3.7391
url https://revistas.unifacs.br/index.php/rsc/article/view/7391
identifier_str_mv 10.36558/rsc.v11i3.7391
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv https://revistas.unifacs.br/index.php/rsc/article/downloadSuppFile/7391/29255
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Revista de Sistemas e Computação - RSC
Revistade Sistemas y Computación
publisher.none.fl_str_mv Revista de Sistemas e Computação - RSC
Revistade Sistemas y Computación
dc.source.none.fl_str_mv Revista de Sistemas e Computação - RSC; v. 11, n. 3 (2021)
Revistade Sistemas y Computación; v. 11, n. 3 (2021)
reponame:Revista de Sistemas e Computação
instname:Universidade Salvador (UNIFACS)
instacron:UNIFACS
instname_str Universidade Salvador (UNIFACS)
instacron_str UNIFACS
institution UNIFACS
reponame_str Revista de Sistemas e Computação
collection Revista de Sistemas e Computação
repository.name.fl_str_mv Revista de Sistemas e Computação - Universidade Salvador (UNIFACS)
repository.mail.fl_str_mv paulo.caetano@unifacs.br || unifacs@nexodoc.com.br
_version_ 1833830805371092992

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