Implicit QR for companion-like pencils

Paola Boito (1) , Yuli Eidelman , Luca Gemignani

1 XLIM-MATHIS - Mathématiques & Sécurité de l'information

A fast implicit QR algorithm for eigenvalue computation of low rank corrections of unitary matrices is adjusted to work with matrix pencils arising from polynomial zero-finding problems. The modified QZ algorithm computes the generalized eigenvalues of certain $ N\times N$ rank structured matrix pencils using $ O(N^2)$ flops and $ O(N)$ memory storage. Numerical experiments and comparisons confirm the effectiveness and the stability of the proposed method. - See more at: http://www.ams.org/journals/mcom/2016-85-300/S0025-5718-2015-03020-8/#sthash.JxbTFYBc.dpuf

Domaines: Analyse numérique [math.NA]

Paola Boito, Yuli Eidelman, Luca Gemignani. Implicit QR for companion-like pencils. Mathematics of Computation, 2016, 85 (300), pp.1753-1774. ⟨10.1090/mcom/3020⟩. ⟨hal-01293222⟩