Modified Gershgorin disks for companion matrices (Q2902839)
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scientific article; zbMATH DE number 6069980
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Modified Gershgorin disks for companion matrices |
scientific article; zbMATH DE number 6069980 |
Statements
22 August 2012
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Gershgorin Disks
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companion matrix
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roots of polynomials
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Ovals of Cassini
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Modified Gershgorin disks for companion matrices (English)
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The eigenvalues of a matrix are contained in the union of its Gershgorin disks. If this matrix is the usual companion matrix of a polynomial, this leads to an inclusion set for the roots of this polynomial. Here it is shown how this set can be improved by using the special form of the companion matrix. This improvement is illustrated by some simple examples. A MATLAB code for showing this improvement is also given.
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