Parallel algorithm for solving penta-diagonal linear systems

摘要

According to the parallel algorithms for solving tridiagonal linear systems, we studied the parallel algorithms for solving penta-diagonal linear systems. In the parallel solutions for tridiagonal linear systems-cyclic reduction method (CR), recursive doubling method (RD) and the partition method (PD), however, only the cyclic reduction algorithm can be used to solve the penta-diagonal linear systems. Compared with the serial algorithm of solving penta-diagonal linear systems-Gaussion elimination, cyclic reduction algorithm has obvious advantages. In this paper, we evaluated these methods by their execution time. According to the measured datas, the cyclic reduction algorithm has been implemented via multi-threads. The efficiency of Cyclic reduction algorithm is more efficient than the Gaussion algorithm by 23.74%.