On Solving Pentadiagonal Linear Systems via Transformations

Many authors have studied numerical algorithms for solving the linear systems of pentadiagonal type. The well-known fast pentadiagonal system solver algorithm is an example of such algorithms. The current paper describes new numerical and symbolic algorithms for solving pentadiagonal linear systems via transformations. The proposed algorithms generalize the algorithms presented in El-Mikkawy and Atlan, 2014. Our symbolic algorithms remove the cases where the numerical algorithms fail. The computational cost of our algorithms is better than those algorithms in literature. Some examples are given in order to illustrate the effectiveness of the proposed algorithms. All experiments are carried out on a computer with the aid of programs written in MATLAB