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A New Algorithm for Computing the Determinant and the Inverse of a Pentadiagonal Toeplitz Matrix

DOI: 10.4236/eng.2013.55A004    3,638 Downloads   5,331 Views   Citations
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ABSTRACT

An effective numerical algorithm for computing the determinant of a pentadiagonal Toeplitz matrix has been proposed by Xiao-Guang Lv and others [1]. The complexity of the algorithm is (9n + 3). In this paper, a new algorithm with the cost of (4n + 6) is presented to compute the determinant of a pentadiagonal Toeplitz matrix. The inverse of a pentadiagonal Toeplitz matrix is also considered.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

Y. Chen, "A New Algorithm for Computing the Determinant and the Inverse of a Pentadiagonal Toeplitz Matrix," Engineering, Vol. 5 No. 5A, 2013, pp. 25-28. doi: 10.4236/eng.2013.55A004.

References

[1] [1] X. G. Lv, T. Z. Huang and J. Le, “A Note on Computing the Inverse and the Determinant of a Pentadiagonal Toeplitz Matrix,” Applied Mathematics and Computation, Vol. 206, No. 1, 2008, pp. 327-331. doi:10.1016/j.amc.2008.09.006
[2] E. Kilic and M. Ei-Mikkawy, “A Computational Algorithm for Special nth Order Pentadiagonal Toeplitz Determinants,” Applied Mathematics and Computation, Vol. 199, No. 2, 2008, pp. 820-822. doi:10.1016/j.amc.2007.10.022
[3] J. M. McNally, “A Fast Algorithm for Solving Diagonally Dominant Symmetric Pentadiagonal Toeplitz Systems,” Journal of Computational and Applied Mathematics, Vol. 234, No. 4, 2010, pp. 995-1005. doi:10.1016/j.cam.2009.03.001
[4] S. S. Nemani, “A Fast Algorithm for Solving Toeplitz Penta-Diagonal Systems,” Applied Mathematics and Computation, Vol. 215, No. 11, 2010, pp. 3830-3838.
[5] Y. H. Chen and C. Y. Yu, “A New Algorithm for Computing the Inverse and the Determinant of a Hessenbert Matrix,” Applied Mathematics and Computation, Vol. 218, 2011, pp. 4433-4436. doi:10.1016/j.amc.2011.10.022
[6] G. H. Golub and C. F. Van Loan, “Matrix Computations,” 3rd Edition, Johns Hopkings University Press, Baltimore and London, 1996, pp. 193-202.

  
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