Implicit QR for Companion-like Pencils
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 zerofinding problems . The modified QZ algorithm computes the generalized eigenvalues of certain NxN rank structured matrix pencils using O(N2) ops and O(N) memory storage. Numerical experiments and comparisons confirm the effectiveness and the stability of the proposed method.
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