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A new recursive algorithm for inverting general periodic pentadiagonal and anti-pentadiagonal matrices. (English) Zbl 1166.65324
Summary: The authors present a new recursive symbolic computational algorithm, that will never break down, for inverting general periodic pentadiagonal and anti-pentadiagonal matrices. It is a natural generalization of the work presented in [{\it M. E. A. El-Mikkawy} and {\it E. D. Rahmo}, Appl. Math. Comput. 204, No. 1, 368--372 (2008; Zbl 1157.65338)]. The algorithm is suited for implementation using computer algebra systems such as Mathematica, Macsyma and Maple. An illustrative example is given.

65F05Direct methods for linear systems and matrix inversion (numerical linear algebra)
Full Text: DOI
[1] Hadj, A. Driss Aiat; Elouafi, M.: A fast numerical algorithm for the inverse of a tridiagonal and pentadiagonal matrix, Appl. math. Comput. 202, 441-445 (2008) · Zbl 1153.65030 · doi:10.1016/j.amc.2008.02.026
[2] Demmel, J. W.: Numerical linear algebra, (1997) · Zbl 0879.65017
[3] Karawia, A. A.: A computational algorithm for solving periodic pentadiagonal linear systems, Appl. math. Comput. 174, 613-618 (2006) · Zbl 1089.65023 · doi:10.1016/j.amc.2005.04.098
[4] El-Mikkawy, M. E. A.; Rahmo, E. D.: A new recursive algorithm for inverting general tridiagonal and anti-tridiagonal matrices, Appl. math. Comput. 204, 368-372 (2008) · Zbl 1157.65338 · doi:10.1016/j.amc.2008.06.053
[5] Zhao, X. I. -Le; Huang, Ting-Zhu: On the inverse of a general pentadiagonal matrix, Appl. math. Comput. 202, 639-646 (2008) · Zbl 1149.65019 · doi:10.1016/j.amc.2008.03.004