Inequalities and bounds for the zeros of polynomials using perron-frobenius and gerschgorin theories

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Abstract

In this paper, disks containing some or all zeros of a complex polynomial or eigenvalues of a complex matrix are developed. These disks are based on extensions of Cauchy classical bounds, Perron-Frobenius theory of positive matrices, and Gerschgorin theory. As a special case, given a real polynomial with real maximum or minimum zero, intervals containing the extreme zeros are developed. Moreover, methods for computing or refining these intervals are derived. Additionally, a closed form singular value decomposition of a characteristic polynomial was derived and utilized to compute new bounds for the zeros of polynomials. Finally, bounds which are based on zero transformation are given.

Original languageEnglish (US)
Pages (from-to)2745-2750
Number of pages6
JournalProceedings of the American Control Conference
Volume3
DOIs
StatePublished - Jan 1 2004
EventProceedings of the 2004 American Control Conference (AAC) - Boston, MA, United States
Duration: Jun 30 2004Jul 2 2004

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