Optimally packed chains of bulges in multishift QR algorithms

DOI10.1145/2559986zbMath1305.65122OpenAlexW2109407035WikidataQ113310310 ScholiaQ113310310MaRDI QIDQ5498688

Daniel Kressner, Bruno Lang, Lars Karlsson

Publication date: 10 February 2015

Published in: ACM Transactions on Mathematical Software (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1145/2559986

zbMATH Keywords

level 3 BLASimplicit shiftsmultishift QR algorithms

Mathematics Subject Classification ID

Numerical computation of eigenvalues and eigenvectors of matrices (65F15)

Related Items (5)

Algorithm 1019: A Task-based Multi-shift QR/QZ Algorithm with Aggressive Early Deflation ⋮ An extended Hamiltonian QR algorithm ⋮ On pole-swapping algorithms for the eigenvalue problem ⋮ A Multishift, Multipole Rational QZ Method with Aggressive Early Deflation ⋮ Rank-Structured QR for Chebyshev Rootfinding

Uses Software

• LAPACK
• BLAS

Cites Work

• Unnamed Item
• On the use of larger bulges in the QR algorithm
• Numerical methods for general and structured eigenvalue problems.
• The Multishift QR Algorithm. Part I: Maintaining Well-Focused Shifts and Level 3 Performance
• The Multishift QR Algorithm. Part II: Aggressive Early Deflation
• Algorithm 953
• A Novel Parallel QR Algorithm for Hybrid Distributed Memory HPC Systems
• The QR Transformation A Unitary Analogue to the LR Transformation--Part 1
• ON A BLOCK IMPLEMENTATION OF HESSENBERG MULTISHIFT QR ITERATION
• LAPACK Users' Guide
• Shifting Strategies for the Parallel $QR$ Algorithm
• A Parallel Implementation of the Nonsymmetric QR Algorithm for Distributed Memory Architectures
• Forward Stability and Transmission of Shifts in the $QR$ Algorithm
• The Matrix Eigenvalue Problem
• Multishift Variants of the QZ Algorithm with Aggressive Early Deflation

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