Implicit QR for rank-structured matrix pencils

Paola Boito (1) , Yuli Eidelman , Luca Gemignani

1 XLIM-DMI - DMI

A fast implicit QR algorithm for eigenvalue computation of low rank corrections of Hermitian matrices is adjusted to work with matrix pencils arising from zerofinding problems for polynomials expressed in Chebyshev-like bases. The modified QZ algorithm computes the generalized eigenvalues of certain N×N rank structured matrix pencils using O(N2) flops and O(N) memory storage. Numerical experiments and comparisons confirm the effectiveness and the stability of the proposed method.

Mots clés: Rank-structured matrix Quasiseparable matrix QZ algorithm Chebyshev approximation Eigenvalue computation Complexity

Domaines: Analyse numérique [math.NA]

Paola Boito, Yuli Eidelman, Luca Gemignani. Implicit QR for rank-structured matrix pencils. BIT Numerical Mathematics, 2014. ⟨hal-01293218⟩