On a block implementation of Hessenberg multishift QR iteration
International Journal of High Speed Computing
Deferred shifting schemes for parallel QR methods
SIAM Journal on Matrix Analysis and Applications
A parallel QR algorithm for the symmetric tridiagonal eigenvalue problem
Journal of Parallel and Distributed Computing
Applied numerical linear algebra
Applied numerical linear algebra
The symmetric eigenvalue problem
The symmetric eigenvalue problem
QR-like algorithms for eigenvalue problems
Journal of Computational and Applied Mathematics - Special issue on numerical analysis 2000 Vol. III: linear algebra
The Multishift QR Algorithm. Part I: Maintaining Well-Focused Shifts and Level 3 Performance
SIAM Journal on Matrix Analysis and Applications
The Multishift QR Algorithm. Part II: Aggressive Early Deflation
SIAM Journal on Matrix Analysis and Applications
Efficient Implementation of the Multishift $QR$ Algorithm for the Unitary Eigenvalue Problem
SIAM Journal on Matrix Analysis and Applications
SIAM Review
The Matrix Eigenvalue Problem: GR and Krylov Subspace Methods
The Matrix Eigenvalue Problem: GR and Krylov Subspace Methods
A multiple shift QR-step for structured rank matrices
Journal of Computational and Applied Mathematics
An Implicit Multishift $QR$-Algorithm for Hermitian Plus Low Rank Matrices
SIAM Journal on Scientific Computing
| Hi-index | 7.29 |
In 1989, Bai and Demmel proposed the multishift QR algorithm for eigenvalue problems. Although the global convergence property of the algorithm (i.e., the convergence from any initial matrix) still remains an open question for general nonsymmetric matrices, in 1992 Jiang focused on symmetric tridiagonal case and gave a global convergence proof for the generalized Rayleigh quotient shifts. In this paper, we propose Wilkinson-like shifts, which reduce to the standard Wilkinson shift in the single shift case, and show a global convergence theorem.