Annals of Functional Analysis

Estimates for the numerical radius and the spectral radius of the Frobenius companion matrix and bounds for the zeros of polynomials

Amer Abu-Omar and Fuad Kittaneh

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Abstract

We apply numerical radius and spectral radius estimates to the Frobenius companion matrices of monic polynomials to derive new bounds for their zeros and give different proofs of some known bounds.

Article information

Source
Ann. Funct. Anal., Volume 5, Number 1 (2014), 56-62.

Dates
First available in Project Euclid: 5 February 2014

Permanent link to this document
https://projecteuclid.org/euclid.afa/1391614569

Digital Object Identifier
doi:10.15352/afa/1391614569

Mathematical Reviews number (MathSciNet)
MR3119112

Zentralblatt MATH identifier
1298.47011

Subjects
Primary: 47A12: Numerical range, numerical radius
Secondary: 15A60: Norms of matrices, numerical range, applications of functional analysis to matrix theory [See also 65F35, 65J05] 26C10: Polynomials: location of zeros [See also 12D10, 30C15, 65H05] 30C15: Zeros of polynomials, rational functions, and other analytic functions (e.g. zeros of functions with bounded Dirichlet integral) {For algebraic theory, see 12D10; for real methods, see 26C10}

Keywords
Frobenius companion matrix zeros of polynomials numerical radius spectral radius inequality

Citation

Abu-Omar, Amer; Kittaneh, Fuad. Estimates for the numerical radius and the spectral radius of the Frobenius companion matrix and bounds for the zeros of polynomials. Ann. Funct. Anal. 5 (2014), no. 1, 56--62. doi:10.15352/afa/1391614569. https://projecteuclid.org/euclid.afa/1391614569


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References

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