Research reports

Years: 2024 2023 2022 2021 2020 2019 2018 2017 2016 2015 2014 2013 2012 2011 2010 2009 2008 2007 2006 2005 2004 2003 2002 2001 2000 1999 1998 1997 1996 1995 1994 1993 1992 1991

Blocked algorithms for the reduction to Hessenberg-triangular form revisited

by B. Kagstroem and D. Kressner and E. S. Quintana-Orti and G. Quintana-Orti

(Report number 2008-17)

Abstract
We present two variants of Moler and Stewart's algorithm for reducing a matrix pair to Hessenberg-triangular (HT) form with increased data locality in the access to the matrices. In one of these variants, a careful reoganization and accumulation of Givens rotations enables the use of efficient level 3 BLAS. Experimental results on four different architectures, representative of current high performance processors, compare the performances of the new variants with those of the implementation of Moler and Stewart's algorithm in subroutine {\tt DGGHRD} from LAPACK, Dackland and Kragstroem's two-stage algorithm for the HT form, and a modified version of the latter which requires considerably less flops.

Keywords: Generalized eigenvalue problems, Hessenberg-triangular form, QZ algorithm, orthogonal transformations, high-performance computing, level 3 BLAS, blocked algorithms.

@Techreport{KKQQ08_381,
  author = {B. Kagstroem and D. Kressner and E. S. Quintana-Orti and G. Quintana-Orti},
  title = {Blocked algorithms for the reduction to Hessenberg-triangular form revisited},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2008-17},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2008/2008-17.pdf },
  year = {2008}
}

Disclaimer
© Copyright for documents on this server remains with the authors. Copies of these documents made by electronic or mechanical means including information storage and retrieval systems, may only be employed for personal use. The administrators respectfully request that authors inform them when any paper is published to avoid copyright infringement. Note that unauthorised copying of copyright material is illegal and may lead to prosecution. Neither the administrators nor the Seminar for Applied Mathematics (SAM) accept any liability in this respect. The most recent version of a SAM report may differ in formatting and style from published journal version. Do reference the published version if possible (see SAM Publications).