Parallelizing the QR algorithm for the unsymmetric algebraic eigenvalue problem: Myths and reality

作     者：Henry, G VandeGeijn, R 

作者机构：UNIV TEXASDEPT COMP SCIAUSTINTX 78712 

出 版 物：《SIAM JOURNAL ON SCIENTIFIC COMPUTING》 (工业与应用数学会科学计算杂志)

年 卷 期：1996年第17卷第4期

页      面：870-883页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

主　　题：parallel computing eigenvalue Schur decomposition QR algorithm 

摘      要：Over the last few years, it has been suggested that the popular QR algorithm for the unsymmetric Schur decomposition does not parallelize. In this paper, we present both positive and negative results on this subject. In theory, asymptotically perfect speedup can be obtained. In practice, reasonable speedup can be obtained on an MIMD distributed memory computer for a relatively small number of processors. However, we also show theoretically that it is impossible for the standard QR algorithm to be scalable. performance of a parallel implementation of the LAPACK DLAHQR routine on the Intel Paragon(TM) system is reported.