Geodesic
Improved initialization of the accelerated and robust QR-like polynomial root-finding
Electronic transactions on numerical analysis, Tome 17 (2004), pp. 195-205
We approximate polynomial roots numerically as the eigenvalues of a unitary diagonal plus rank-one matrix. We rely on our earlier adaptation of the algorithm, which exploits the semiseparable matrix structure to

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approximate the eigenvalues in a fast and robust way, but we substantially improve the performance of the resulting algorithm at the initial stage, as confirmed by our numerical tests.
Classification : 65H17, 65F15
Keywords: iteration, eigenvalue computation, polynomial roots, semiseparable matrices, DFT, FFT, moe- $$###$$§$$###$$ bius transformation 
@article{ETNA_2004__17__a2,
     author = {Bini,  Dario A. and Gemignani,  Luca and Pan,  Victor Y.},
     title = {Improved initialization of the accelerated and robust {QR-like} polynomial root-finding},
     journal = {Electronic transactions on numerical analysis},
     pages = {195--205},
     year = {2004},
     volume = {17},
     zbl = {1065.65065},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_2004__17__a2/}
}
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AU  - Gemignani,  Luca
AU  - Pan,  Victor Y.
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JO  - Electronic transactions on numerical analysis
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%0 Journal Article
%A Bini,  Dario A.
%A Gemignani,  Luca
%A Pan,  Victor Y.
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%J Electronic transactions on numerical analysis
%D 2004
%P 195-205
%V 17
%U http://geodesic.mathdoc.fr/item/ETNA_2004__17__a2/
%G en
%F ETNA_2004__17__a2
Bini,  Dario A.; Gemignani,  Luca; Pan,  Victor Y. Improved initialization of the accelerated and robust QR-like polynomial root-finding. Electronic transactions on numerical analysis, Tome 17 (2004), pp. 195-205. http://geodesic.mathdoc.fr/item/ETNA_2004__17__a2/