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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.

BibTeX

@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}
}

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First published: May 2008 (PDF)file_download

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