External selective orthogonalization for the Lanczos algorithm in distributed memory environments

作     者：Cooper, A Szularz, M Weston, J 

作者机构：Univ Ulster Sch Informat & Software Engn Coleraine BT52 1SA Londonderry North Ireland 

出 版 物：《PARALLEL COMPUTING》 (并行计算)

年 卷 期：2001年第27卷第7期

页      面：913-923页

核心收录：

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

主　　题：Lanczos algorithm restarting deflation reorthogonalization MPP 

摘      要：The k-step explicit restart Lanczos algorithm, LExpRes, for the computation of a few of the extreme eigenpairs of large, usually sparse, symmetric matrices, computes one eigenpair at a time using a deflation technique in which each Lanczos vector generated is orthogonalized against all previously converged eigenvectors. The computation of the inner products associated with this external orthogonalization often creates a bottleneck in parallel distributed memory environments. In this paper methods are proposed which significantly reduce this computational overhead in LExpRes, thereby effectively improving its efficiency. The performances of these methods on the Cray-T3D and the Cray-T3E are assessed and critically compared with that of the original algorithm. (C) 2001 Elsevier Science B.V. All rights reserved.