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Algorithm 506: HQR3 and EXCHNG: Fortran Subroutines for Calculating and Ordering the Eigenvalues of a Real Upper Hessenberg Matrix F2

Algorithm 506: HQR3 and EXCHNG: Fortran Subroutines for Calculating and Ordering the Eigenvalues... ALGORITHM 506 HQR3 and EXCHNG: Fortran Subroutines for Calculating and Ordering the Eigenvalues of a Real Upper Hessenberg Matrix EF2] G. W. STEWART University of Maryland Key Words and Phrases: eigenvalue, QR-algorithm CR Categories: 5.14 Language: Fortran DESCRIPTION 1. Usage HQR3 is a Fortran subroutine to reduce a real upper Hessenberg matrix A to quasitriangular form B b y a unitary similarity transformation U: The diagonal of B consists of 1X1 and 2 X 2 blocks as illustrated below: o x x x x x X X X [;xxxx B = UTA U. X 0 0 x x 0 0 0 x 0 0 0 x The 1X1 blocks contain the real eigenvalues of A, and the 2 X 2 blocks contain the complex eigenvalues, a conjugate pair to each block. The blocks are ordered so that the eigenvalues appear in descending order of absolute value along the diagonal. The transformation U is postmultiplied into an array V, which presumably contains earlier transformations performed on A. The decomposition produced b y HQR3 differs from the one produced b y the E I S P A C K subroutine HQR2 [2] in t h a t the eigenvalues of http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png ACM Transactions on Mathematical Software (TOMS) Association for Computing Machinery

Algorithm 506: HQR3 and EXCHNG: Fortran Subroutines for Calculating and Ordering the Eigenvalues of a Real Upper Hessenberg Matrix F2

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References (7)

Publisher
Association for Computing Machinery
Copyright
Copyright © 1976 by ACM Inc.
ISSN
0098-3500
DOI
10.1145/355694.355700
Publisher site
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Abstract

ALGORITHM 506 HQR3 and EXCHNG: Fortran Subroutines for Calculating and Ordering the Eigenvalues of a Real Upper Hessenberg Matrix EF2] G. W. STEWART University of Maryland Key Words and Phrases: eigenvalue, QR-algorithm CR Categories: 5.14 Language: Fortran DESCRIPTION 1. Usage HQR3 is a Fortran subroutine to reduce a real upper Hessenberg matrix A to quasitriangular form B b y a unitary similarity transformation U: The diagonal of B consists of 1X1 and 2 X 2 blocks as illustrated below: o x x x x x X X X [;xxxx B = UTA U. X 0 0 x x 0 0 0 x 0 0 0 x The 1X1 blocks contain the real eigenvalues of A, and the 2 X 2 blocks contain the complex eigenvalues, a conjugate pair to each block. The blocks are ordered so that the eigenvalues appear in descending order of absolute value along the diagonal. The transformation U is postmultiplied into an array V, which presumably contains earlier transformations performed on A. The decomposition produced b y HQR3 differs from the one produced b y the E I S P A C K subroutine HQR2 [2] in t h a t the eigenvalues of

Journal

ACM Transactions on Mathematical Software (TOMS) – Association for Computing Machinery

Published: Sep 1, 1976

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