The transmission of shifts and shift blurring in the QR algorithm

DOI10.1016/0024-3795(95)00545-5zbMath0871.65027OpenAlexW2000570676MaRDI QIDQ1923181

David S. Watkins

Publication date: 1 October 1997

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0024-3795(95)00545-5

zbMATH Keywords

performanceeigenvaluesnumerical experimentsparallel computationrounding errorsmultishift QR algorithm

Mathematics Subject Classification ID

Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Parallel numerical computation (65Y05)

Related Items

The $QR$ Steps with Perfect Shifts ⋮ A QR algorithm with variable iteration multiplicity ⋮ An extended Hamiltonian QR algorithm ⋮ A new framework for implicit restarting of the Krylov-Schur algorithm ⋮ Computing the Jordan Structure of an Eigenvalue ⋮ Deflating invariant subspaces for rank structured pencils ⋮ Rational QZ steps with perfect shifts ⋮ Numerical solution of linear eigenvalue problems ⋮ On pole-swapping algorithms for the eigenvalue problem ⋮ Eigenvalue computation for unitary rank structured matrices ⋮ The periodic QR algorithm is a disguised QR algorithm ⋮ Computing the eigenvectors of nonsymmetric tridiagonal matrices ⋮ Implicit QR algorithms for palindromic and even eigenvalue problems ⋮ A Multishift, Multipole Rational QZ Method with Aggressive Early Deflation ⋮ \(QR\)-like algorithms for eigenvalue problems

Uses Software

• LAPACK
• EISPACK
• testmatrix

Cites Work

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• Convergence of algorithms of decomposition type for the eigenvalue problem
• On Hamiltonian and symplectic Hessenberg forms
• Matrix eigensystem routines. EISPACK guide extension
• A class of Hamiltonian-symplectic methods for solving the algebraic Riccati equation
• A multishift algorithm for the numerical solution of algebraic Riccati equations
• The QR Transformation A Unitary Analogue to the LR Transformation--Part 1
• Chasing Algorithms for the Eigenvalue Problem
• ON A BLOCK IMPLEMENTATION OF HESSENBERG MULTISHIFT QR ITERATION
• Theory of Decomposition and Bulge-Chasing Algorithms for the Generalized Eigenvalue Problem
• Shifting Strategies for the Parallel $QR$ Algorithm
• Forward Stability and Transmission of Shifts in the $QR$ Algorithm
• Parallelizing the QR Algorithm for the Unsymmetric Algebraic Eigenvalue Problem: Myths and Reality

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