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Algorithm 710: FORTRAN subroutines for computing the eigenvalues and eigenvectors of a general matrix by reduction to general tridiagonal form

Editor: Robert J. Renka Authors:

J. J. Dongarra,

G. A. Geist,

C. H. RomineAuthors Info & Claims

ACM Transactions on Mathematical Software (TOMS), Volume 18, Issue 4

Pages 392 - 400

https://doi.org/10.1145/138351.138352

Published: 01 December 1992 Publication History

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Abstract

This paper describes programs to reduce a nonsymmetric matrix to tridiagonal form, to compute the eigenvalues of the tridiagonal matrix, to improve the accuracy of an eigenvalue, and to compute the corresponding eigenvector. The intended purpose of the software is to find a few eigenpairs of a dense nonsymmetric matrix faster and more accurately than previous methods. The performance and accuracy of the new routines are compared to two EISPACK paths: RG and HQR-INVIT. The results show that the new routines are more accurate and also faster if less than 20 percent of the eigenpairs are needed.

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eigenvalues and eigenvectors of a general matrix Gams: d4a

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References

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Cited By

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Van Dooren PLaudadio TMastronardi N(2021)Computing the Eigenvectors of Nonsymmetric Tridiagonal MatricesComputational Mathematics and Mathematical Physics10.1134/S096554252105008061:5(733-749)Online publication date: 1-Jul-2021
https://doi.org/10.1134/S0965542521050080
Zhao WYan ZFang X(2014)Application of an improved BHESS-BR method to the small signal stability analysis of power systemsInternational Transactions on Electrical Energy Systems10.1002/etep.186525:4(661-677)Online publication date: 14-Jan-2014
https://doi.org/10.1002/etep.1865
Langou JLangou JLuszczek PKurzak JButtari ADongarra JHorner-Miller B(2006)Exploiting the performance of 32 bit floating point arithmetic in obtaining 64 bit accuracy (revisiting iterative refinement for linear systems)Proceedings of the 2006 ACM/IEEE conference on Supercomputing10.1145/1188455.1188573(113-es)Online publication date: 11-Nov-2006
https://dl.acm.org/doi/10.1145/1188455.1188573
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Index Terms

Algorithm 710: FORTRAN subroutines for computing the eigenvalues and eigenvectors of a general matrix by reduction to general tridiagonal form

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Published In

cover image ACM Transactions on Mathematical Software

ACM Transactions on Mathematical Software Volume 18, Issue 4

Dec. 1992

117 pages

ISSN:0098-3500

EISSN:1557-7295

DOI:10.1145/138351

Editor:
Robert J. Renka
Univ. of North Texas, Denton

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 01 December 1992

Published in TOMS Volume 18, Issue 4

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Van Dooren PLaudadio TMastronardi N(2021)Computing the Eigenvectors of Nonsymmetric Tridiagonal MatricesComputational Mathematics and Mathematical Physics10.1134/S096554252105008061:5(733-749)Online publication date: 1-Jul-2021
https://doi.org/10.1134/S0965542521050080
Zhao WYan ZFang X(2014)Application of an improved BHESS-BR method to the small signal stability analysis of power systemsInternational Transactions on Electrical Energy Systems10.1002/etep.186525:4(661-677)Online publication date: 14-Jan-2014
https://doi.org/10.1002/etep.1865
Langou JLangou JLuszczek PKurzak JButtari ADongarra JHorner-Miller B(2006)Exploiting the performance of 32 bit floating point arithmetic in obtaining 64 bit accuracy (revisiting iterative refinement for linear systems)Proceedings of the 2006 ACM/IEEE conference on Supercomputing10.1145/1188455.1188573(113-es)Online publication date: 11-Nov-2006
https://dl.acm.org/doi/10.1145/1188455.1188573
Langou JLangou JLuszczek PKurzak JButtari ADongarra J(2006)Exploiting the Performance of 32 bit Floating Point Arithmetic in Obtaining 64 bit Accuracy (Revisiting Iterative Refinement for Linear Systems)ACM/IEEE SC 2006 Conference (SC'06)10.1109/SC.2006.30(50-50)Online publication date: Nov-2006
https://doi.org/10.1109/SC.2006.30
Howell GDiaa N(2005)Algorithm 841: BHESS: Gaussian reduction to a similar banded Hessenberg formACM Transactions on Mathematical Software10.1145/1055531.105553931:1(166-185)Online publication date: 1-Mar-2005
https://dl.acm.org/doi/10.1145/1055531.1055539
Bini DGemignani LTisseur F(2005)The Ehrlich--Aberth Method for the Nonsymmetric Tridiagonal Eigenvalue ProblemSIAM Journal on Matrix Analysis and Applications10.1137/S089547980342978827:1(153-175)Online publication date: 1-May-2005
https://dl.acm.org/doi/10.1137/S0895479803429788
Sidje RBurrage K(2005)QRT: A QR-Based Tridiagonalization Algorithm for Nonsymmetric MatricesSIAM Journal on Matrix Analysis and Applications10.1137/04061247626:3(878-900)Online publication date: Jan-2005
https://doi.org/10.1137/040612476
Henry GWatkins DDongarra J(2002)A Parallel Implementation of the Nonsymmetric QR Algorithm for Distributed Memory ArchitecturesSIAM Journal on Scientific Computing10.1137/S106482759732516524:1(284-311)Online publication date: 1-Jan-2002
https://dl.acm.org/doi/10.1137/S1064827597325165
Nikolajsen J(2000)An Improved Laguerre Eigensolver for Unsymmetric MatricesSIAM Journal on Scientific Computing10.1137/S106482759834963X22:3(822-834)Online publication date: 1-Jan-2000
https://dl.acm.org/doi/10.1137/S106482759834963X
Watkins D(1998)Bulge Exchanges in Algorithms of QR TypeSIAM Journal on Matrix Analysis and Applications10.1137/S089547989629995019:4(1074-1096)Online publication date: 1-Oct-1998
https://dl.acm.org/doi/10.1137/S0895479896299950
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Abstract

Supplementary Material

References

Cited By

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Recommendations

Algorithm 343: eigenvalues and eigenvectors of a real general matrix

A QL Procedure for Computing the Eigenvalues of Complex Symmetric Tridiagonal Matrices

FORTRAN subroutines for general Toeplitz systems

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