The BR Eigenvalue algorithm

G. A. Geist; G. W. Howell; D. S. Watkins

doi:10.1137/S0895479897317077

The BR Eigenvalue algorithm

G. A. Geist
, G. W. Howell
, D. S. Watkins

Research output: Contribution to journal › Article › peer-review

10 Scopus citations

Abstract

The BR algorithm, a new method for calculating the eigenvalues of an upper Hessenberg matrix, is introduced. It is a bulge-chasing algorithm like the QR algorithm, but, unlike the QR algorithm, it is well adapted to computing the eigenvalues of the narrow-band, nearly tridiagonal matrices generated by the look-ahead Lanczos process. This paper describes the BR algorithm and gives numerical evidence that it works well in conjunction with the Lanczos process. On the biggest problems run so far, the BR algorithm beats the QR algorithm by a factor of 30-60 in computing time and a factor of over 100 in matrix storage space.

Original language	English
Pages (from-to)	1083-1098
Number of pages	16
Journal	SIAM Journal on Matrix Analysis and Applications
Volume	20
Issue number	4
DOIs	https://doi.org/10.1137/S0895479897317077
State	Published - Jul 1999

Keywords

Eigenvalue computation
QR algorithm
Unsymmetric Lanczos process

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AU - Howell, G. W.

AU - Watkins, D. S.

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AB - The BR algorithm, a new method for calculating the eigenvalues of an upper Hessenberg matrix, is introduced. It is a bulge-chasing algorithm like the QR algorithm, but, unlike the QR algorithm, it is well adapted to computing the eigenvalues of the narrow-band, nearly tridiagonal matrices generated by the look-ahead Lanczos process. This paper describes the BR algorithm and gives numerical evidence that it works well in conjunction with the Lanczos process. On the biggest problems run so far, the BR algorithm beats the QR algorithm by a factor of 30-60 in computing time and a factor of over 100 in matrix storage space.

KW - Eigenvalue computation

KW - QR algorithm

KW - Unsymmetric Lanczos process

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JF - SIAM Journal on Matrix Analysis and Applications

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The BR Eigenvalue algorithm

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