Implicit QR for companion-like pencils

P. Boito; Y. Eidelman; L. Gemignani

doi:10.1090/mcom/3020

Implicit QR for companion-like pencils

P. Boito, Y. Eidelman, L. Gemignani

School of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

6 Scopus citations

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 × 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.

Original language	English
Pages (from-to)	1753-1774
Number of pages	22
Journal	Mathematics of Computation
Volume	85
Issue number	300
DOIs	https://doi.org/10.1090/mcom/3020
State	Published - 2016

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10.1090/mcom/3020

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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 × 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.",

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AB - 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 × 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.

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Implicit QR for companion-like pencils

Abstract

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