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Tytuł artykułu

On decomposition of k-tridiagonal ℓ-Toeplitz matrices and its applications

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We consider a k-tridiagonal ℓ-Toeplitz matrix as one of generalizations of a tridiagonal Toeplitz matrix. In the present paper, we provide a decomposition of the matrix under a certain condition. By the decomposition, the matrix is easily analyzed since one only needs to analyze the small matrix obtained from the decomposition. Using the decomposition, eigenpairs and arbitrary integer powers of the matrix are easily shown as applications.
Wydawca
Czasopismo
Rocznik
Tom
3
Numer
1
Opis fizyczny
Daty
otrzymano
2015-06-25
zaakceptowano
2015-09-03
online
2015-10-05
Twórcy
autor
  • Graduate School of Information Science & Technology, Aichi Prefectural University, Japan
autor
  • Graduate School of Engineering, Nagoya University, Japan
autor
  • Graduate School of Information Science & Technology, Aichi Prefectural University, Japan
Bibliografia
  • ---
  • [1] R. Á lvarez-Nodarse, J. Petronilho, N.R. Quintero, On some tridiagonal k-Toeplitzmatrices: algebraic and analytical aspects.Applications, J. Comput. Appl. Math., 184, 2 (2005), 518-537.
  • [2] J.W. Demmel, Applied Numerical Linear Algebra, SIAM, Philadelphia (1997).
  • [3] M.E.A. El-Mikkawy, A generalized symbolic Thomas algorithm, Appl. Math., 3, 4 (2012), 342-345.[Crossref]
  • [4] M.E.A. El-Mikkawy, T. Sogabe, A new family of k-Fibonacci numbers, Appl. Math. Comput., 215, 12 (2010), 4456-4461.
  • [5] C.F. Fischer, R.A. Usmani, Properties of some tridiagonal matrices and their application to boundary value problems, SIAM,J. Numer. Anal., 6, 1 (1969), 127-142.[Crossref]
  • [6] C.M. da Fonseca, J. Petronilho, Explicit inverse of a tridiagonal k-Toeplitz matrix, Numer. Math., 100, 3 (2005), 457-482.
  • [7] E. Kilic, On a constant-diagonals matrix, Appl. Math. Comput., 204, 1 (2008), 184-190.[WoS]
  • [8] E. Kırklar, F. Yılmaz, A note on k-tridiagonal k-Toeplitz matrices, Ala. J. Math., 39, (2015), 1-4.
  • [9] C.D. Meyer, Matrix Analysis and Applied Linear Algebra, SIAM, Philadelphia (2004).
  • [10] A. Ohashi, T.S. Usuda, T. Sogabe, F. Yılmaz, On tensor product decomposition of k-tridiagonal Toeplitz matrices, Int. J. Pureand Appl. Math., 103, 3 (2015), 537-545.
  • [11] T. Sogabe, M.E.A. El-Mikkawy, Fast block diagonalization of k-tridiagonal matrices, Appl. Math. Comput., 218, 6 (2011),2740-2743.
  • [12] J. Wittenburg, Inverses of tridiagonal Toeplitz and periodic matrices with applications to mechanics, J. Appl. Math. Mech.,62, 4 (1998), 575-587.
  • [13] T. Yamamoto, Inversion formulas for tridiagonalmatrices with applications to boundary value problems, Numer. Funct. Anal.Optim., 22, 3-4 (2001), 357-385.[Crossref]
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_1515_spma-2015-0019
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