The QR Algorithm Revisited

Authors:
David S. Watkins
Affiliations:
-
Venue:
SIAM Review
Year:
2008

Citing 0
Cited 5

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An Implicit Multishift $QR$-Algorithm for Hermitian Plus Low Rank Matrices

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A Novel Parallel QR Algorithm for Hybrid Distributed Memory HPC Systems

SIAM Journal on Scientific Computing
Chasing Bulges or Rotations? A Metamorphosis of the QR-Algorithm

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A Wilkinson-like multishift QR algorithm for symmetric eigenvalue problems and its global convergence

Journal of Computational and Applied Mathematics

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Abstract

The $QR$ algorithm is still one of the most important methods for computing eigenvalues and eigenvectors of matrices. Most discussions of the $QR$ algorithm begin with a very basic version and move by steps toward the versions of the algorithm that are actually used. This paper outlines a pedagogical path that leads directly to the implicit multishift $QR$ algorithms that are used in practice, bypassing the basic $QR$ algorithm completely.