ON A BLOCK IMPLEMENTATION OF HESSENBERG MULTISHIFT QR ITERATION

作     者：Zhaojun Bai James Demmel 

作者机构：Courant Institute of Mathematical Sciences New York University 251 Mercer Street New York NY 10012 USA 

出 版 物：《International Journal of High Speed Computing》 

年 卷 期：1989年第1卷第1期

页      面：97-112页

主　　题：Eigenvalue Hessenberg matrix QR algorithm BLAS Parallel algorithm 

摘      要：The usual QR algorithm for finding the eigenvalues of a Hessenberg matrix H is based on vector-vector operations, e.g. adding a multiple of one row to another. The opportunities for parallelism in such an algorithm are limited. In this paper, we describe a reorganization of the QR algorithm to permit either matrix-vector or matrix-matrix operations to be performed, both of which yield more efficient implementations on vector and parallel machines. The idea is to chase a k by k bulge rather than a 1 by 1 or 2 by 2 bulge as in the standard QR algorithm. We report our preliminary numerical experiments on the CONVEX C-1 and CYBER 205 vector machines.