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Rapid convergence of the shifted QR algorithm on symmetric matrices was shown more than fifty years ago.
On the convergence of the Rayleigh quotient iteration for the computation of the characteristic roots and vectors. I
Alexander M Ostrowski · 1957
Earlier work this paper cites.
A geometric proof of convergence for the QR method
Hendrik Jan Buurema · 1958
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The QR transformation a unitary analogue to the LR transformation—Part 1
John GF Francis · 1961
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The QR transformation—Part 2
John GF Francis · 1962
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On some algorithms for the solution of the complete eigenvalue problem
Vera N Kublanovskaya · 1962
Earlier work this paper cites.
Singular and invariant matrices under the QR transformation
Beresford Parlett · 1966
Earlier work this paper cites.
On the convergence of a practical QR algorithm
Beresford N Parlett and William Kahan · 1968
Earlier work this paper cites.
Global convergence of tridiagonal QR algorithm with origin shifts
James H Wilkinson · 1968
Earlier work this paper cites.
The shifted QR algorithm for Hermitian matrices
Theodorus J Dekker and Joseph F. Traub · 1971
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Normal Hessenberg and moment matrices
Beresford Parlett · 1973
Earlier work this paper cites.
The Rayleigh quotient iteration and some generalizations for nonnormal matrices
Beresford N Parlett · 1974
Earlier work this paper cites.
Global convergence of the QR algorithm for unitary matrices with some results for normal matrices
Patricia J Eberlein and C. P. Huang · 1975
Earlier work this paper cites.
A new proof of global convergence for the tridiagonal QL algorithm
Walter Hoffmann and Beresford N Parlett · 1978
Earlier work this paper cites.
Three research problems in numerical linear algebra
Cleve B Moler · 1978
Earlier work this paper cites.
I: Functional analysis
Michael Reed and Barry Simon · 1980
Earlier work this paper cites.
Understanding the QR algorithm
David S Watkins · 1982
Earlier work this paper cites.
On a block implementation of Hessenberg multishift QR iteration
Zhaojun Bai and James Demmel · 1989
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The dynamics of Rayleigh quotient iteration
Steve Batterson and John Smillie · 1989
Earlier work this paper cites.
Convergence of the shifted QR algorithm on 3 × \times 3 normal matrices
Steve Batterson · 1990
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Rayleigh quotient iteration for nonsymmetric matrices
Steve Batterson and John Smillie · 1990
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Linear convergence in the shifted QR algorithm
Steve Batterson and David Day · 1992
Cited alongside, same era.
A note on the double-shift QL algorithm
Jiang Erxiong · 1992
Cited alongside, same era.
Forward instability of tridiagonal QR
Beresford N Parlett and Jian Le · 1993
Cited alongside, same era.
Convergence of the Francis shifted QR algorithm on normal matrices
Steve Batterson · 1994
Cited alongside, same era.
Dynamical analysis of numerical systems
Steve Batterson · 1995
Cited alongside, same era.
Forward stability and transmission of shifts in the QR algorithm
David S Watkins · 1995
Cited alongside, same era.
How the QR algorithm fails to converge and how to fix it
Smoothed analysis of algorithms: Why the simplex algorithm usually takes polynomial time
Daniel A Spielman and Shang-Hua Teng · 2004
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Lapack 3.1 xHSEQR: Tuning and implementation notes on the small bulge multi-shift QR algorithm with aggressive early deflation
Ralph Byers · 2007
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The matrix eigenvalue problem: GR and Krylov subspace methods
David S Watkins · 2007
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Linear algebra algorithms as dynamical systems
Moody T Chu · 2008
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Approximate diagonalization
E. Brian Davies · 2008
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The QR algorithm revisited
David S Watkins · 2008
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David Day · 1996
Cited alongside, same era.
Matrix computations. Johns Hopkins studies in the mathematical sciences, 1996
Gene H Golub and Charles F Van Loan · 1996
Cited alongside, same era.
Applied numerical linear algebra
James W Demmel · 1997
Cited alongside, same era.
Complexity theory and numerical analysis
Steve Smale · 1997
Cited alongside, same era.
Numerical linear algebra
Lloyd N Trefethen and David Bau III · 1997
Cited alongside, same era.
Guest editors’ introduction: The top 10 algorithms
Jack Dongarra and Francis Sullivan · 2000
Cited alongside, same era.
The QR algorithm: 50 years later its genesis by John Francis and Vera Kublanovskaya and subsequent developments
Gene Golub and Frank Uhlig · 2009
Later among the works it cites.
A Wilkinson-like multishift QR algorithm for symmetric eigenvalue problems and its global convergence
Kensuke Aishima, Takayasu Matsuo, Kazuo Murota, and Masaaki Sugihara · 2012
Later among the works it cites.
Dynamics of the symmetric eigenvalue problem with shift strategies
Ricardo S Leite, Nicolau C Saldanha, and Carlos Tomei · 2013
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Logarithmic potentials with external fields
Edward B Saff and Vilmos Totik · 2013
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Variants of the QR algorithm
Cleve Moler · 2014
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The Princeton companion to applied mathematics
Nicholas J Higham, Mark R Dennis, Paul Glendinning, Paul A Martin, Fadil Santosa, and Jared Tanner · 2015
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A stable, polynomial-time algorithm for the eigenpair problem
Diego Armentano, Carlos Beltrán, Peter Bürgisser, Felipe Cucker, and Michael Shub · 2018
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Jess Banks, Jorge Garza-Vargas, Archit Kulkarni, and Nikhil Srivastava · 2020
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On the real Davies’ conjecture
Vishesh Jain, Ashwin Sah, and Mehtaab Sawhney · 2020
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Gaussian regularization of the pseudospectrum and Davies’ conjecture
Jess Banks, Archit Kulkarni, Satyaki Mukherjee, and Nikhil Srivastava · 2021
Closest in time.
Personal communication
Daniel Kressner · 2021
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Pseudospectral shattering, the sign function, and diagonalization in nearly matrix multiplication time
Jess Banks, Jorge Garza-Vargas, Archit Kulkarni, and Nikhil Srivastava · 2022
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Global linear convergence of Hessenberg shifted QR II: Numerical stability
Jess Banks, Jorge Garza-Vargas, and Nikhil Srivastava · 2022
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Global linear convergence of Hessenberg shifted QR III: Approximate Ritz values via shifted inverse iteration
Jess Banks, Jorge Garza-Vargas, and Nikhil Srivastava · 2022
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