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A neural network-based approach for approximating arbitrary roots of polynomials

2021Journal article Open access
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dc.contributor.authorFreitas, Diogo
dc.contributor.authorLopes, Luiz
dc.contributor.authorDias, Fernando Morgado
dc.date.accessioned2021-10-20T12:39:05Z
dc.date.available2021-10-20T12:39:05Z
dc.date.issued2021
dc.description.abstractFinding arbitrary roots of polynomials is a fundamental problem in various areas of science and engineering. A myriad of methods was suggested to address this problem, such as the sequential Newton’s method and the Durand–Kerner (D–K) simultaneous iterative method. The sequential iterative methods, on the one hand, need to use a deflation procedure in order to compute approximations to all the roots of a given polynomial, which can produce inaccurate results due to the accumulation of rounding errors. On the other hand, the simultaneous iterative methods require good initial guesses to converge. However, Artificial Neural Networks (ANNs) are widely known by their capacity to find complex mappings between the dependent and independent variables. In view of this, this paper aims to determine, based on comparative results, whether ANNs can be used to compute approximations to the real and complex roots of a given polynomial, as an alternative to simultaneous iterative algorithms like the D–K method. Although the results are very encouraging and demonstrate the viability and potentiality of the suggested approach, the ANNs were not able to surpass the accuracy of the D–K method. The results indicated, however, that the use of the approximations computed by the ANNs as the initial guesses for the D–K method can be beneficial to the accuracy of this methodpt_PT
dc.description.versioninfo:eu-repo/semantics/publishedVersionpt_PT
dc.identifier.citationFreitas, D., Lopes Guerreiro, L., & Morgado-Dias, F. (2021). A neural network-based approach for approximating arbitrary roots of polynomials. Mathematics, 9(4), 317. https://doi.org/10.3390/math9040317pt_PT
dc.identifier.doi10.3390/math9040317pt_PT
dc.identifier.urihttp://hdl.handle.net/10400.13/3739
dc.language.isoengpt_PT
dc.peerreviewedyespt_PT
dc.publisherMDPIpt_PT
dc.relationLaboratory of Robotics and Engineering Systems
dc.rights.urihttp://creativecommons.org/licenses/by/4.0/pt_PT
dc.subjectPolynomial rootspt_PT
dc.subjectArtificial neural networkspt_PT
dc.subjectParticle swarm optimizationpt_PT
dc.subjectDurand– Kerner methodpt_PT
dc.subjectPerformance analysispt_PT
dc.subject.pt_PT
dc.subjectFaculdade de Ciências Exatas e da Engenhariapt_PT
dc.titleA neural network-based approach for approximating arbitrary roots of polynomialspt_PT
dc.typejournal article
dspace.entity.typePublication
oaire.awardTitleLaboratory of Robotics and Engineering Systems
oaire.awardURIinfo:eu-repo/grantAgreement/FCT/6817 - DCRRNI ID/UIDB%2F50009%2F2020/PT
oaire.citation.issue4pt_PT
oaire.citation.startPage317pt_PT
oaire.citation.titleMathematicspt_PT
oaire.citation.volume9pt_PT
oaire.fundingStream6817 - DCRRNI ID
person.familyNameTeixeira Freitas
person.familyNameGuerreiro Lopes
person.familyNameMorgado-Dias
person.givenNameDiogo Nuno
person.givenNameLuiz Carlos
person.givenNameFernando
person.identifieryfy16oUAAAAJ
person.identifierB-4961-2016
person.identifier.ciencia-id9C13-AF9C-25F3
person.identifier.ciencia-id4A18-1DCB-4862
person.identifier.ciencia-id7B14-DF07-AA6D
person.identifier.orcid0000-0002-2351-8676
person.identifier.orcid0000-0002-6145-8520
person.identifier.orcid0000-0001-7334-3993
person.identifier.scopus-author-id57205501523
project.funder.identifierhttp://doi.org/10.13039/501100001871
project.funder.nameFundação para a Ciência e a Tecnologia
rcaap.rightsopenAccesspt_PT
rcaap.typearticlept_PT
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