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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 [M. E. A. El-Mikkawy and 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.
MSC:
65F05Direct methods for linear systems and matrix inversion (numerical linear algebra)
Software:
Maple
References:
[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