# 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

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topA. 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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- [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. Pure and Appl. Math., 103, 3 (2015), 537-545. Zbl1327.15018
- [11] T. Sogabe, M.E.A. El-Mikkawy, Fast block diagonalization of k-tridiagonal matrices, Appl. Math. Comput., 218, 6 (2011), 2740-2743. Zbl06043893
- [12] J. Wittenburg, Inverses of tridiagonal Toeplitz and periodic matrices with applications to mechanics, J. Appl. Math. Mech., 62, 4 (1998), 575-587.
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