The eigenvalues of r-periodic tridiagonal matrices by factorization of some recursive sequences

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dc.contributor.authorSahin, Murat
dc.contributor.authorYilmaz, Semih
dc.date.accessioned2020-06-25T18:29:37Z
dc.date.available2020-06-25T18:29:37Z
dc.date.issued2018
dc.departmentKırıkkale Üniversitesi
dc.description.abstractWe introduce r-periodic tridiagonal matrices for given integer r >= 2. In which the entries on the principle diagonal can be any r-periodic sequence. If the entries on the principle diagonal are equal then the calculation of the eigenvalues of corresponding tridiagonal matrices is relatively easy, but when the entries are not equal, the calculation becomes much more difficult. So, some explicit formulas could be given only for the eigenvalues of certain types of the 2-periodic tridiagonal matrices so far. We give a new algorithm to find the eigenvalues of certain r-periodic tridiagonal matrices and give some results by implementing it in a symbolic programming language. Our algorithm also finds the zeros of some families of polynomials with integer coefficients. The degree of these polynomials can be chosen very high. Also, we give some new properties of the generalized continuant and then we solve an open problem by determining a complex factorization of certain r-periodic sequences. Finally, we generalize existing results by giving the explicit formulas for the eigenvalues of some r-periodic tridiagonal matrices for r = 2, 3 and 4. (C) 2017 Elsevier B.V. All rights reserved.en_US
dc.identifier.citationclosedAccessen_US
dc.identifier.doi10.1016/j.cam.2017.11.034
dc.identifier.endpage113en_US
dc.identifier.issn0377-0427
dc.identifier.issn1879-1778
dc.identifier.scopus2-s2.0-85039806656
dc.identifier.scopusqualityQ1
dc.identifier.startpage99en_US
dc.identifier.urihttps://doi.org/10.1016/j.cam.2017.11.034
dc.identifier.urihttps://hdl.handle.net/20.500.12587/7396
dc.identifier.volume335en_US
dc.identifier.wosWOS:000424722100007
dc.identifier.wosqualityQ1
dc.indekslendigikaynakWeb of Science
dc.indekslendigikaynakScopus
dc.language.isoen
dc.publisherElsevier Science Bven_US
dc.relation.ispartofJournal Of Computational And Applied Mathematics
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanıen_US
dc.rightsinfo:eu-repo/semantics/closedAccessen_US
dc.subjectTridiagonal matricesen_US
dc.subjectEigenvaluesen_US
dc.subjectCharacteristic polynomialsen_US
dc.subjectConditional recurrencesen_US
dc.subjectContinued fractionsen_US
dc.subjectContinuantsen_US
dc.titleThe eigenvalues of r-periodic tridiagonal matrices by factorization of some recursive sequencesen_US
dc.typeArticle

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