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A real QZ algorithm for structured companion pencils |
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| Authors: | P Boito Y Eidelman L Gemignani |
| Affiliation: | 1.Faculté des Sciences et Techniques,XLIM-DMI UMR CNRS 7252,Limoges,France;2.Laboratoire LIP (CNRS, ENS Lyon, Inria, UCBL), CNRS,Université de Lyon,Lyon Cedex 07,France;3.Raymond and Beverly Sackler Faculty of Exact Sciences, School of Mathematical Sciences,Tel-Aviv University,Ramat-Aviv,Israel;4.Dipartimento di Informatica,Università di Pisa,Pisa,Italy |
| Abstract: | We design a fast implicit real QZ algorithm for eigenvalue computation of structured companion pencils arising from linearizations of polynomial rootfinding problems. The modified QZ algorithm computes the generalized eigenvalues of an \(N\times N\) structured matrix pencil using O(N) flops per iteration and O(N) memory storage. Numerical experiments and comparisons confirm the effectiveness and the stability of the proposed method. |
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