Algorithm 953: Parallel Library Software for the Multishift QR Algorithm with Aggressive Early Deflation

作     者：Granat, Robert Kagstrom, Bo Kressner, Daniel Shao, Meiyue 

作者机构：Umea Univ Dept Comp Sci SE-90187 Umea Sweden Umea Univ HPC2N SE-90187 Umea Sweden Ecole Polytech Fed Lausanne MATHICSE CH-1015 Lausanne Switzerland 

出 版 物：《ACM TRANSACTIONS ON MATHEMATICAL SOFTWARE》 (美国计算机学会数学软件汇刊)

年 卷 期：2015年第41卷第4期

页      面：29-29页

核心收录：

学科分类：08[工学] 0835[工学-软件工程] 0701[理学-数学] 0812[工学-计算机科学与技术（可授工学、理学学位）] 

基　　金：Swedish Research Council [A0581501] UMIT Research Lab via an EU Mal 2 project Swedish Research Council 

主　　题：Algorithms Performance Multishift QR algorithm aggressive early deflation parallel algorithms distributed memory architectures 

摘      要：Library software implementing a parallel small-bulge multishift QR algorithm with Aggressive Early Deflation (AED) targeting distributed memory high-performance computing systems is presented. Starting from recent developments of the parallel multishift QR algorithm [Granat et al., SIAM J. Sci. Comput. 32(4), 2010], we describe a number of algorithmic and implementation improvements. These include communication avoiding algorithms via data redistribution and a refined strategy for balancing between multishift QR sweeps and AED. Guidelines concerning several important tunable algorithmic parameters are provided. As a result of these improvements, a computational bottleneck within AED has been removed in the parallel multishift QR algorithm. A performance model is established to explain the scalability behavior of the new parallel multishift QR algorithm. Numerous computational experiments confirm that our new implementation significantly outperforms previous parallel implementations of the QR algorithm.