Bounds for the zeros of polynomials from eigenvalues and singular values of some companion matrices (Q1379083)
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scientific article; zbMATH DE number 1116045
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Bounds for the zeros of polynomials from eigenvalues and singular values of some companion matrices |
scientific article; zbMATH DE number 1116045 |
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Bounds for the zeros of polynomials from eigenvalues and singular values of some companion matrices (English)
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23 July 1998
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Let \(P_n(x)\) be a monic polynomial of degree \(n\geq 1\). The author uses two types of generalized companion matrices to obtain estimates for the zeros of the polynomial \(P_n\), mainly by the application of Gershgorin's theorem to the companion matrices and using majorization relations between the eigenvalues and singular values of a matrix. Some classical and recently found bounds for zeros are improved and some new bounds are obtained.
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bound for zeros of polynomials
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companion matrices
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eigenvalues
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Gershgorin's theorem
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singular values
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0.9687093
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0.93025017
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0.92760664
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0.92713255
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0.92471135
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0.91872585
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