A Novel Parallel Algorithm Based on the Gram-Schmidt Method for Tridiagonal Linear Systems of Equations

作     者：Ghodsi, Seyed Roholah Taeibi-Rahni, Mohammad 

作者机构：IAU Dept Mech & Aerosp Engn Sci & Res Branch Tehran *** Iran 

出 版 物：《MATHEMATICAL PROBLEMS IN ENGINEERING》 (Math. Probl. Eng.)

年 卷 期：2010年第2010卷第1期

核心收录：

学科分类：08[工学] 0701[理学-数学] 

主　　题：Parallel algorithms 

摘      要：This paper introduces a new parallel algorithm based on the Gram-Schmidt orthogonalization method. This parallel algorithm can find almost exact solutions of tridiagonal linear systems of equations in an efficient way. The system of equations is partitioned proportional to number of processors, and each partition is solved by a processor with a minimum request from the other partitions data. The considerable reduction in data communication between processors causes interesting speedup. The relationships between partitions approximately disappear if some columns are switched. Hence, the speed of computation increases, and the computational cost decreases. Consequently, obtained results show that the suggested algorithm is considerably scalable. In addition, this method of partitioning can significantly decrease the computational cost on a single processor and make it possible to solve greater systems of equations. To evaluate the performance of the parallel algorithm, speedup and efficiency are presented. The results reveal that the proposed algorithm is practical and efficient.