Canonical decomposition of Hessenberg matrices

Parlett, Beresford Ν.

doi:10.1090/s0025-5718-1967-0228519-6

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1979

2024

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Cited by 15 publications

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“…1 right for an illustration of the form of a typical blockD j,j ofD. Similar canonical normal forms were used in [25,26] to study the convergence of the QR-iteration in the complex setting. The structure of Y ∈ ω(X 0 ) has the following properties:…”

Section: Nmentioning

confidence: 99%

Dynamics of the QR-flow for upper Hessenberg real matrices

Tatjer¹,

Vieiro²

2021

Discrete &Amp; Continuous Dynamical Systems - B

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We investigate the main phase space properties of the QR-flow when restricted to upper Hessenberg matrices. A complete description of the linear behavior of the equilibrium matrices is given. The main result classifies the possible α-and ω-limits of the orbits for this system. Furthermore, we characterize the set of initial matrices for which there is convergence towards an equilibrium matrix. Several numerical examples show the different limit behavior of the orbits and illustrate the theory.

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Section: Nmentioning

confidence: 99%