A novel algorithm and its parallelization for solving nearly penta-diagonal linear systems

Abstract

In the current paper, a new serial algorithm for solving nearly penta-diagonal linear systems is presented. The computational cost of the algorithm is less than or almost equal to those of recent successful algorithms [J. Jia, Q. Kong, and T. Sogabe, A fast numerical algorithm for solving nearly penta-diagonal linear systems, Int. J. Comput. Math. 89 (2012), pp. 851–860; X.G. Lv and J. Le, A note on solving nearly penta-diagonal linear systems, Appl. Math. Comput. 204 (2008), pp. 707–712; S.N. Neossi Nguetchue and S. Abelman, A computational algorithm for solving nearly penta-diagonal linear systems, Appl. Math. Comput. 203 (2008), pp. 629–634]. Moreover, it is suitable for developing its parallel algorithms. One of the parallel algorithms is given and is shown to be promising. The implementation of the algorithms using Computer Algebra Systems such as MATLAB and MAPLE is straightforward. Two numerical examples are given in order to illustrate the validity and efficiency of our algorithms.

Keywords:

• nearly penta-diagonal matrices
• parallel algorithm
• linear systems
• Crout LU decomposition
• computer algebra systems

2010 AMS Subject Classifications:

• 15A09
• 15A23
• 65F30
• 33F10

Acknowledgements

This work was supported by the Natural Science Foundation of China (NSFC) under grant 11071192 and the International Science and Technology Cooperation Program of China under grant 2010DFA14700. The authors thank the anonymous referees whose comments substantially enhanced the quality of the paper.