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Mathematical Problems in Engineering
Volume 2015, Article ID 232456, 9 pages
Research Article

On Solving Pentadiagonal Linear Systems via Transformations

1Department of Statistics and Operations Researches, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia
2Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt
3Computer Science Unit, Deanship of Educational Services, Qassim University, P.O. Box 6595, Buraidah 51452, Saudi Arabia

Received 4 January 2015; Revised 18 March 2015; Accepted 18 March 2015

Academic Editor: George S. Dulikravich

Copyright © 2015 S. S. Askar and A. A. Karawia. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.