On formulae for the determinant of symmetric pentadiagonal Toeplitz matrices

We show that the characteristic polynomial of a symmetric pentadiagonal Toeplitz matrix is the product of two polynomials given explicitly in terms of the Chebyshev polynomials. Mathematics Subject Classification 15B05 * 65F40 * 33C45

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Bibliographic Details
Published inArabian Journal of Mathematics Vol. 7; no. 2; pp. 91 - 99
Main Author Elouafi, Mohamed
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 01.06.2018
Springer
Springer Nature B.V
Subjects
Chebyshev approximation
Determinants (Mathematics)
Differential equations
Mathematical analysis
Mathematical research
Mathematics
Mathematics and Statistics
Matrices (Mathematics)
Matrix methods
Polynomials
Signal processing
15B05
65F40
33C45
Online AccessGet full text
ISSN2193-5343
2193-5351
2193-5351
DOI10.1007/s40065-017-0194-0

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Abstract We show that the characteristic polynomial of a symmetric pentadiagonal Toeplitz matrix is the product of two polynomials given explicitly in terms of the Chebyshev polynomials. Mathematics Subject Classification 15B05 * 65F40 * 33C45
AbstractList We show that the characteristic polynomial of a symmetric pentadiagonal Toeplitz matrix is the product of two polynomials given explicitly in terms of the Chebyshev polynomials.
We show that the characteristic polynomial of a symmetric pentadiagonal Toeplitz matrix is the product of two polynomials given explicitly in terms of the Chebyshev polynomials. Mathematics Subject Classification 15B05 * 65F40 * 33C45
Audience Academic
Author Elouafi, Mohamed
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crossref_primary_10_1080_03081087_2019_1708845
crossref_primary_10_1134_S0001434623010054
crossref_primary_10_3336_gm_56_2_05
crossref_primary_10_3390_math8071056
Cites_doi 10.1142/9700
10.1016/j.camwa.2016.01.027
10.1088/0266-5611/21/6/005
10.1016/j.laa.2011.05.025
10.1007/978-3-319-49182-0_11
10.1007/BF02575838
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Copyright The Author(s) 2017
COPYRIGHT 2018 Springer
Arabian Journal of Mathematics is a copyright of Springer, (2017). All Rights Reserved.
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References Grenander, Szeg ö (CR9) 1984
Elouafi (CR7) 2014; 229
Barrera, Grudsky (CR1) 2017; 259
CR4
Doman (CR3) 2015
Jia, Yang, Li (CR10) 2016; 71
Elouafi (CR5) 2011; 435
Fasino (CR8) 1988; 25
Elouafi (CR6) 2013; 219
Chu, Diele, Ragnion (CR2) 2005; 21
Mason, Handscomb (CR11) 2003
MT Chu (194_CR2) 2005; 21
JC Mason (194_CR11) 2003
D Fasino (194_CR8) 1988; 25
M Barrera (194_CR1) 2017; 259
JT Jia (194_CR10) 2016; 71
BGS Doman (194_CR3) 2015
M Elouafi (194_CR5) 2011; 435
194_CR4
M Elouafi (194_CR7) 2014; 229
M Elouafi (194_CR6) 2013; 219
U Grenander (194_CR9) 1984
References_xml – year: 2015
  ident: CR3
  publication-title: The Classical Orthogonal Polynomials
  doi: 10.1142/9700
– volume: 71
  start-page: 1036
  year: 2016
  end-page: 1044
  ident: CR10
  article-title: On a homogeneous recurrence relation for the determinants of general pentadiagonal Toeplitz matrices
  publication-title: Comput. Math. Appl.
  doi: 10.1016/j.camwa.2016.01.027
– year: 2003
  ident: CR11
  publication-title: Chebyshev Polynomials
– volume: 21
  start-page: 1879
  year: 2005
  end-page: 1894
  ident: CR2
  article-title: On the inverse problem of constructing symmetric pentadiagonal Toeplitz matrices from three largest eigenvalues
  publication-title: Inverse Probl.
  doi: 10.1088/0266-5611/21/6/005
– volume: 219
  start-page: 4789
  issue: 9
  year: 2013
  end-page: 4791
  ident: CR6
  article-title: A note for an explicit formula for the determinant of pentadiagonal and heptadiagonal symmetric Toeplitz matrices
  publication-title: Appl. Math. Comput.
– volume: 435
  start-page: 2986
  year: 2011
  end-page: 2998
  ident: CR5
  article-title: An eigenvalue localization theorem for pentadiagonal symmetric Toeplitz matrices
  publication-title: Linear Algebra Appl.
  doi: 10.1016/j.laa.2011.05.025
– volume: 259
  start-page: 179
  year: 2017
  end-page: 212
  ident: CR1
  article-title: Asymptotics of eigenvalues for pentadiagonal symmetric Toeplitz matrices
  publication-title: Oper. Theory Adv. Appl.
  doi: 10.1007/978-3-319-49182-0_11
– volume: 25
  start-page: 301
  year: 1988
  end-page: 310
  ident: CR8
  article-title: Spectral and structural properties of some pentadiagonal symmetric matrices
  publication-title: Calcolo
  doi: 10.1007/BF02575838
– ident: CR4
– volume: 229
  start-page: 27
  issue: 25
  year: 2014
  end-page: 33
  ident: CR7
  article-title: On a relationship between Chebyshev polynomials and Toeplitz determinants
  publication-title: Appl. Math. Comput.
– year: 1984
  ident: CR9
  publication-title: Toeplitz Forms and their Applications
– volume-title: Toeplitz Forms and their Applications
  year: 1984
  ident: 194_CR9
– volume: 259
  start-page: 179
  year: 2017
  ident: 194_CR1
  publication-title: Oper. Theory Adv. Appl.
  doi: 10.1007/978-3-319-49182-0_11
– volume-title: The Classical Orthogonal Polynomials
  year: 2015
  ident: 194_CR3
  doi: 10.1142/9700
– volume: 21
  start-page: 1879
  year: 2005
  ident: 194_CR2
  publication-title: Inverse Probl.
  doi: 10.1088/0266-5611/21/6/005
– volume-title: Chebyshev Polynomials
  year: 2003
  ident: 194_CR11
– volume: 25
  start-page: 301
  year: 1988
  ident: 194_CR8
  publication-title: Calcolo
  doi: 10.1007/BF02575838
– volume: 71
  start-page: 1036
  year: 2016
  ident: 194_CR10
  publication-title: Comput. Math. Appl.
  doi: 10.1016/j.camwa.2016.01.027
– volume: 435
  start-page: 2986
  year: 2011
  ident: 194_CR5
  publication-title: Linear Algebra Appl.
  doi: 10.1016/j.laa.2011.05.025
– ident: 194_CR4
– volume: 219
  start-page: 4789
  issue: 9
  year: 2013
  ident: 194_CR6
  publication-title: Appl. Math. Comput.
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  start-page: 27
  issue: 25
  year: 2014
  ident: 194_CR7
  publication-title: Appl. Math. Comput.
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SubjectTerms Chebyshev approximation
Determinants (Mathematics)
Differential equations
Mathematical analysis
Mathematical research
Mathematics
Mathematics and Statistics
Matrices (Mathematics)
Matrix methods
Polynomials
Signal processing
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Title On formulae for the determinant of symmetric pentadiagonal Toeplitz matrices
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