Implicit QR for companion-like pencils
Paola Boito, Y. Eidelman, Luca Gemignani · Mathematics of Computation · 2015
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 × N N\times N rank structured matrix pencils using O ( N 2 ) O(N^2) flops and O ( N ) O(N) memory storage. Numerical experiments and comparisons confirm the effectiveness and the stability of the proposed method.