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Symbolic algorithm for inverting cyclic pentadiagonal matrices recursively - derivation and implementation. (English) Zbl 1189.65053
Summary: By using parallel computing along with recursion, we describe a reliable symbolic computational algorithm for inverting cyclic pentadiagonal matrices. The algorithm is implemented in MAPLE. Two other symbolic algorithms are developed and the computational costs for all algorithms are given. An example is presented for the sake of illustration.

MSC:
65F05Direct methods for linear systems and matrix inversion (numerical linear algebra)
68W30Symbolic computation and algebraic computation
15A09Matrix inversion, generalized inverses
Software:
PENT; Maple
References:
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[3]Lv, X. -G.; Le, J.: A note on solving nearly pentadiagonal linear systems, Appl. math. Comput. 204, 707-712 (2008) · Zbl 1157.65339 · doi:10.1016/j.amc.2008.07.012
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[6]Sogabe, T.: New algorithms for solving periodic tridiagonal and periodic pentadiagonal linear systems, Appl. math. Comput. 202, 850-856 (2008) · Zbl 1151.65022 · doi:10.1016/j.amc.2008.03.030
[7]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
[8]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
[9]Demmel, J. W.: Numerical linear algebra, SIAM (1997) · Zbl 0879.65017
[10]El-Mikkawy, M.; Rahmo, E.: 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
[11]El-Mikkawy, M.: A fast algorithm for evaluating nth order tri-diagonal determinants, J. comput. Appl. math. 166, 581-584 (2004) · Zbl 1051.65062 · doi:10.1016/j.cam.2003.08.044
[12]El-Mikkawy, M.: A fast and reliable algorithm for evaluating nth order pentadiagonal determinants, Appl. math. Comput. 202, 210-215 (2008) · Zbl 1151.65038 · doi:10.1016/j.amc.2008.01.032
[13]El-Mikkawy, M.; Rahmo, E.: A new recursive algorithm for inverting general periodic pentadiagonal and anti-pentadiagonal matrices, Appl. math. Comput. 207, 164-170 (2009) · Zbl 1166.65324 · doi:10.1016/j.amc.2008.10.010
[14]El-Mikkawy, M.: A note on a three-term recurrence for a tridiagonal matrix, Appl. math. Comput. 139, 503-511 (2003) · Zbl 1078.65533 · doi:10.1016/S0096-3003(02)00212-6