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We develop a framework for proving rapid convergence of shifted QR algorithms which use Ritz values as shifts, in finite arithmetic.
Global convergence of tridiagonal qr algorithm with origin shifts
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On a block implementation of Hessenberg multishift QR iteration
Zhaojun Bai and James Demmel · 1989
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Ji-Guang Sun · 1991
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Forward stability and transmission of shifts in the QR algorithm
David S Watkins · 1995
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Backward stability of the QR algorithm
Francoise Tisseur · 1996
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The transmission of shifts and shift blurring in the QR algorithm
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Rajendra Bhatia · 2007
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A randomized homotopy for the Hermitian eigenpair problem
Diego Armentano and Felipe Cucker · 2015
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A stable, polynomial-time algorithm for the eigenpair problem
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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 · 2020
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A Krylov–Schur algorithm for large eigenproblems
Gilbert W Stewart · 2002
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On the use of larger bulges in the QR algorithm
Daniel Kressner · 2005
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Global convergence of Hessenberg shifted QR I: Dynamics
Jess Banks, Jorge Garza-Vargas, and Nikhil Srivastava · 2022
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Global convergence of Hessenberg shifted QR III: Backward approximate Ritz values via inverse iteration
Jess Banks, Jorge Garza-Vargas, and Nikhil Srivastava · 2022
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