求解大规模矩阵特征问题的并行算法研究-武汉大学学报·信息科学版.PDF

36 6 2010 3 Vol.36 No.6 Computer Engineering March 2010 ·· 2010 A TP301.6 ( 100190) Arnoldi Arnoldi Arnoldi KD-50-I Arnoldi Study on Parallel Algorithm for Solving Large Matrix Eigenproblem ZHAO Tao, CHI Xue-bin, LU Zhong-hua, ZHAO Yong-hua (Supercomputing Center, Computer Network Information Center, Chinese Academy of Sciences, Beijing 100190) AbstractBased on the parallel algorithm for restarted Arnoldi method by using data parallel model, a parallel algorithm for refined restarted Arnoldi method is presented. To impair the negative impact on parallel performance due to weak scalability, Tthe parallel algorithm presented implements parallel computing refined vectors by using task graph model and reduces the communication cost. As a result, the algorithm achieves parallel computing efficiently. Numerical experiments on KD-50-I show that the parallel algorithm presented performs good scalability and efficiency. Key wordsmatrix eigenvalue; Arnoldi algorithm; parallel computing; refined vector 1 A V V H m m+1 m mn, V ∈Cn×m H ∈Cm×m m m Hessenberg VH v 0 , V =( V , v ) m m+1 m+ 1 m m+ 1 (m+1)×m