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Fiedler-Comrade and Fiedler-Chebyshev pencils

Noferini, V and Pérez, J (2016) 'Fiedler-Comrade and Fiedler-Chebyshev pencils.' SIAM Journal on Matrix Analysis and Applications, 37 (4). 1600 - 1624. ISSN 0895-4798

ChebyshevFiedler_SIMAX.pdf - Accepted Version

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Fiedler pencils are a family of strong linearizations for polynomials expressed in the monomial basis, that include the classical Frobenius companion pencils as special cases. We generalize the definition of a Fiedler pencil from monomials to a larger class of orthogonal polynomial bases. In particular, we derive Fiedler-comrade pencils for two bases that are extremely important in practical applications: the Chebyshev polynomials of the first and second kind. The new approach allows one to construct linearizations having limited bandwidth: a Chebyshev analogue of the pentadiagonal Fiedler pencils in the monomial basis. Moreover, our theory allows for linearizations of square matrix polynomials expressed in the Chebyshev basis (and in other bases), regardless of whether the matrix polynomial is regular or singular, and for recovery formulas for eigenvectors, and minimal indices and bases.

Item Type: Article
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Science and Health > Mathematical Sciences, Department of
Depositing User: Vanni Noferini
Date Deposited: 21 Feb 2017 14:24
Last Modified: 30 Mar 2021 16:15

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