New algorithms for solving periodic tridiagonal and periodic pentadiagonal linear systems

Recently, an efficient computational algorithm for solving periodic pentadiagonal linear systems has been proposed by Karawia [A.A. Karawia, A computational algorithm for solving periodic pentadiagonal linear systems, Appl. Math. Comput. 174 (2006) 613–618]. The algorithm is based on the LU factorization of the periodic pentadiagonal matrix. In this paper, new algorithms are presented for solving periodic pentadiagonal linear systems based on the use of any pentadiagonal linear solver. In addition, an efficient way of evaluating the determinant of a periodic pentadiagonal matrix is discussed. The corresponding results in this paper can be readily obtained for solving periodic tridiagonal linear systems.