The periodic QR algorithm is a disguised QR algorithm

DOI10.1016/j.laa.2003.06.014zbMath1119.65023OpenAlexW1986219281MaRDI QIDQ2502889

Daniel Kressner

Publication date: 13 September 2006

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

Full work available at URL: https://infoscience.epfl.ch/record/165570/files/pqrequalqr.pdf

zbMATH Keywords

eigenvaluematrix productsQR algorithmHessenberg formblock cyclic matrices

Mathematics Subject Classification ID

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

Related Items (5)

Bifurcations in periodic integrodifference equations in \(C(\Omega)\): II. Discrete torus bifurcations ⋮ A symmetric structure-preserving {\(\Gamma\)}QR algorithm for linear response eigenvalue problems ⋮ The matrix equation \(X + AX^TB = C\): Conditions for unique solvability and a numerical algorithm for its solution ⋮ A periodic Krylov-Schur algorithm for large matrix products ⋮ Structured Eigenvalue Problems

Cites Work

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• The weak and strong stability of algorithms in numerical linear algebra
• General framework, stability and error analysis for numerical stiff boundary value methods
• The transmission of shifts and shift blurring in the QR algorithm
• Exponential splittings of products of matrices and accurately computing singular values of long products
• Matrix Algorithms
• A General Matrix Eigenvalue Algorithm
• Structured Backward Error and Condition of Generalized Eigenvalue Problems
• Numerical solution of the discrete-time periodic Riccati equation
• On the use of periodicity properties for the efficient numerical solution of certain Markov chains
• Bidiagonalization of Matrices and Solution of Linear Equations

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