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Mathematics of Computation

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Implicit QR for companion-like pencils


Authors: P. Boito, Y. Eidelman and L. Gemignani
Journal: Math. Comp. 85 (2016), 1753-1774
MSC (2010): Primary 65F15, 65H17
DOI: https://doi.org/10.1090/mcom/3020
Published electronically: August 31, 2015
MathSciNet review: 3471106
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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 zero-finding problems. The modified QZ algorithm computes the generalized eigenvalues of certain $ N\times N$ rank structured matrix pencils using $ O(N^2)$ flops and $ O(N)$ memory storage. Numerical experiments and comparisons confirm the effectiveness and the stability of the proposed method.


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Additional Information

P. Boito
Affiliation: XLIM–DMI, UMR CNRS 7252, Faculté des Sciences et Techniques, 123 av. A. Thomas, 87060 Limoges, France
Email: paola.boito@unilim.fr

Y. Eidelman
Affiliation: School of Mathematical Sciences, Raymond and Beverly Sackler Faculty of Exact Sciences, Tel-Aviv University, Ramat-Aviv, 69978, Israel
Email: eideyu@post.tau.ac.il

L. Gemignani
Affiliation: Dipartimento di Informatica, Università di Pisa, Largo Bruno Pontecorvo 3, 56127 Pisa, Italy
Email: l.gemignani@di.unipi.it

DOI: https://doi.org/10.1090/mcom/3020
Received by editor(s): January 29, 2014
Received by editor(s) in revised form: October 8, 2014, and December 6, 2014
Published electronically: August 31, 2015
Additional Notes: This work was partially supported by MIUR, grant number 20083KLJEZ
Article copyright: © Copyright 2015 American Mathematical Society