Implicit QR for companion-like pencils

Boito, P.; Eidelman, Y.; Gemignani, L.

doi:10.1090/mcom/3020

Implicit QR for companion-like pencils
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by P. Boito, Y. Eidelman and L. Gemignani PDF

Math. Comp. 85 (2016), 1753-1774 Request permission

Abstract:

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.

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