research-article

Blocked algorithms for the reduction to Hessenberg-triangular form revisited

Authors:

E.S. Quintana-Ortí,

G. Quintana-OrtíAuthors Info & Claims

Volume 48, Issue 3

Pages 563 - 584

https://doi.org/10.1007/s10543-008-0180-1

Published: 01 September 2008 Publication History

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 reorganization 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 DGGHRD from LAPACK, Dackland and Kågström’s two-stage algorithm for the HT form, and a modified version of the latter which requires considerably less flops.

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Cited By

Bosner N(2021)Parallel reduction of four matrices to condensed form for a generalized matrix eigenvalue algorithmNumerical Algorithms10.1007/s11075-020-00883-z86:1(153-178)Online publication date: 1-Jan-2021
https://dl.acm.org/doi/10.1007/s11075-020-00883-z
Kabir KHaidar ATomov SDongarra JWatson LWeinbub JSosonkina MThacker W(2015)Performance analysis and design of a hessenberg reduction using stabilized blocked elementary transformations for new architecturesProceedings of the Symposium on High Performance Computing10.5555/2872599.2872616(135-142)Online publication date: 12-Apr-2015
https://dl.acm.org/doi/10.5555/2872599.2872616
Bosner N(2015)Efficient algorithm for simultaneous reduction to the $$m$$-Hessenberg-triangular-triangular formBIT10.1007/s10543-014-0516-y55:3(677-703)Online publication date: 1-Sep-2015
https://dl.acm.org/doi/10.1007/s10543-014-0516-y

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cover image BIT

BIT Volume 48, Issue 3

Sep 2008

216 pages

ISSN:0006-3835

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Copyright © 2008 Springer Science + Business Media B.V.

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BIT Computer Science and Numerical Mathematics

United States

Publication History

Published: 01 September 2008

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Cited By

Bosner N(2021)Parallel reduction of four matrices to condensed form for a generalized matrix eigenvalue algorithmNumerical Algorithms10.1007/s11075-020-00883-z86:1(153-178)Online publication date: 1-Jan-2021
https://dl.acm.org/doi/10.1007/s11075-020-00883-z
Kabir KHaidar ATomov SDongarra JWatson LWeinbub JSosonkina MThacker W(2015)Performance analysis and design of a hessenberg reduction using stabilized blocked elementary transformations for new architecturesProceedings of the Symposium on High Performance Computing10.5555/2872599.2872616(135-142)Online publication date: 12-Apr-2015
https://dl.acm.org/doi/10.5555/2872599.2872616
Bosner N(2015)Efficient algorithm for simultaneous reduction to the $$m$$-Hessenberg-triangular-triangular formBIT10.1007/s10543-014-0516-y55:3(677-703)Online publication date: 1-Sep-2015
https://dl.acm.org/doi/10.1007/s10543-014-0516-y

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