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

A. Ohashi; T. Sogabe; T.S. Usuda

Special Matrices (2015)

  • Volume: 3, Issue: 1, page 200-206, electronic only
  • ISSN: 2300-7451

Abstract

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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.

How to cite

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A. Ohashi, T. Sogabe, and T.S. Usuda. "On decomposition of k-tridiagonal ℓ-Toeplitz matrices and its applications." Special Matrices 3.1 (2015): 200-206, electronic only. <http://eudml.org/doc/275951>.

@article{A2015,
abstract = {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.},
author = {A. Ohashi, T. Sogabe, T.S. Usuda},
journal = {Special Matrices},
keywords = {k-tridiagonal ℓ-Toeplitz matrix; decomposition; tensor product; eigenpairs; integer powers; -tridiagonal -Toeplitz matrix},
language = {eng},
number = {1},
pages = {200-206, electronic only},
title = {On decomposition of k-tridiagonal ℓ-Toeplitz matrices and its applications},
url = {http://eudml.org/doc/275951},
volume = {3},
year = {2015},
}

TY - JOUR
AU - A. Ohashi
AU - T. Sogabe
AU - T.S. Usuda
TI - On decomposition of k-tridiagonal ℓ-Toeplitz matrices and its applications
JO - Special Matrices
PY - 2015
VL - 3
IS - 1
SP - 200
EP - 206, electronic only
AB - 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.
LA - eng
KW - k-tridiagonal ℓ-Toeplitz matrix; decomposition; tensor product; eigenpairs; integer powers; -tridiagonal -Toeplitz matrix
UR - http://eudml.org/doc/275951
ER -

References

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  3. [2] J.W. Demmel, Applied Numerical Linear Algebra, SIAM, Philadelphia (1997). 
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  5. [4] M.E.A. El-Mikkawy, T. Sogabe, A new family of k-Fibonacci numbers, Appl. Math. Comput., 215, 12 (2010), 4456-4461. Zbl1193.11012
  6. [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] Zbl0176.46802
  7. [6] C.M. da Fonseca, J. Petronilho, Explicit inverse of a tridiagonal k-Toeplitz matrix, Numer. Math., 100, 3 (2005), 457-482. Zbl1076.15011
  8. [7] E. Kilic, On a constant-diagonals matrix, Appl. Math. Comput., 204, 1 (2008), 184-190. [WoS] Zbl1159.65047
  9. [8] E. Kırklar, F. Yılmaz, A note on k-tridiagonal k-Toeplitz matrices, Ala. J. Math., 39, (2015), 1-4. Zbl06577919
  10. [9] C.D. Meyer, Matrix Analysis and Applied Linear Algebra, SIAM, Philadelphia (2004). 
  11. [10] A. Ohashi, T.S. Usuda, T. Sogabe, F. Yılmaz, On tensor product decomposition of k-tridiagonal Toeplitz matrices, Int. J. Pure and Appl. Math., 103, 3 (2015), 537-545. Zbl1327.15018
  12. [11] T. Sogabe, M.E.A. El-Mikkawy, Fast block diagonalization of k-tridiagonal matrices, Appl. Math. Comput., 218, 6 (2011), 2740-2743. Zbl06043893
  13. [12] J. Wittenburg, Inverses of tridiagonal Toeplitz and periodic matrices with applications to mechanics, J. Appl. Math. Mech., 62, 4 (1998), 575-587. 
  14. [13] T. Yamamoto, Inversion formulas for tridiagonalmatrices with applications to boundary value problems, Numer. Funct. Anal. Optim., 22, 3-4 (2001), 357-385. [Crossref] 

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