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

DOI10.1016/j.cam.2011.04.012zbMath1247.65046OpenAlexW2121197356MaRDI QIDQ432772

Kensuke Aishima, Kazuo Murota, Takayasu Matsuo, Masaaki Sugihara

Publication date: 4 July 2012

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cam.2011.04.012

zbMATH Keywords

global convergencesymmetric eigenvalue problemsymmetric tridiagonal matrixWilkinson-like multishift QR algorithm

Mathematics Subject Classification ID

Computational methods for sparse matrices (65F50) Numerical computation of eigenvalues and eigenvectors of matrices (65F15)

Related Items (3)

A shift strategy for superquadratic convergence in the dqds algorithm for singular values ⋮ Unstructured quotient fixed modes and decentralised stabilisability ⋮ On computation of real eigenvalues of matrices via the Adomian decomposition

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Convergence of algorithms of decomposition type for the eigenvalue problem
• A multiple shift \(QR\)-step for structured rank matrices
• A new look at the Lanczos algorithm for solving symmetric systems of linear equations
• A note on the double-shift \(QL\) algorithm
• \(QR\)-like algorithms for eigenvalue problems
• Global convergence of tridiagonal QR algorithm with origin shifts
• Normal Hessenberg and moment matrices
• The Multishift QR Algorithm. Part I: Maintaining Well-Focused Shifts and Level 3 Performance
• The Multishift QR Algorithm. Part II: Aggressive Early Deflation
• An Implicit Multishift $QR$-Algorithm for Hermitian Plus Low Rank Matrices
• ON A BLOCK IMPLEMENTATION OF HESSENBERG MULTISHIFT QR ITERATION
• Deferred Shifting Schemes for Parallel QR Methods
• A New Proof of Global Convergence for the Tridiagonal $QL$ Algorithm
• Efficient Implementation of the Multishift $QR$ Algorithm for the Unitary Eigenvalue Problem
• The Matrix Eigenvalue Problem
• The QR Algorithm Revisited

This page was built for publication: A Wilkinson-like multishift QR algorithm for symmetric eigenvalue problems and its global convergence