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In this paper, we present two novel symbolic computational algorithms to solve periodic pentadiagonal (PP) linear systems. These two algorithms are based on a special matrix decomposition and the use of any fast pentadiagonal linear solver, respectively. Some numerical examples are given in order to demonstrate the performance of the proposed algorithms and their competitiveness with existing algorithms. All of the experiments are performed on a computer workstation with the aid of programs written in MATLAB. [ABSTRACT FROM AUTHOR]