A new recursive algorithm for inverting general periodic pentadiagonal and anti-pentadiagonal matrices Moawwad El-Mikkawy * , El-Desouky Rahmo Mathematics Department, Faculty of Science, Mansoura University, Mansoura 35516, Egypt article info Keywords: Periodic pentadiagonal matrix Periodic anti-pentadiagonal matrix LU factorization Inverse matrix abstract In the current article, 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, E.D. Rahmo, A new recursive algorithm for inverting general tridiago- nal and anti-tridiagonal matrices, Appl. Math. Comput. 204 (2008) 368–372]. The algo- rithm is suited for implementation using computer algebra systems (CAS) such as Mathematica, Macsyma and Maple. An illustrative example is given. Ó 2008 Elsevier Inc. All rights reserved. 1. Introduction The n  n general periodic pentadiagonal and anti-pentadiagonal matrices, denoted, respectively, by P and T, take the forms: P ¼ d 1 a 1 A 1 0  0 b 1 b 2 d 2 a 2 A 2 . . . 0 B 3 b 3 d 3 a 3 A 3 . . . . . . 0 . . . . . . . . . . . . . . . 0 . . . . . . . . . . . . . . . . . . A n2 0 . . . B n1 b n1 d n1 a n1 a n 0  0 B n b n d n 2 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 4 3 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 5 ð1:1Þ 0096-3003/$ - see front matter Ó 2008 Elsevier Inc. All rights reserved. doi:10.1016/j.amc.2008.10.010 * Corresponding author. E-mail addresses: mikkawy@yahoo.com (M. El-Mikkawy), desoukyr@yahoo.com (E.-D. Rahmo). Applied Mathematics and Computation 207 (2009) 164–170 Contents lists available at ScienceDirect Applied Mathematics and Computation journal homepage: www.elsevier.com/locate/amc