Approximate greatest common divisor of many polynomials and pseudo-spectrum

Fatouros, S., Karcanias, N., Christou, D. & Papadopoulos, P. (2013). Approximate greatest common divisor of many polynomials and pseudo-spectrum. System, Structure and Control, 5(1), pp. 623-628. doi: 10.3182/20130204-3-FR-2033.00113

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The paper is concerned with establishing the links between the approximate GCD of a set of polynomials and the notion of the pseudo-spectrum defined on a set of polynomials. By examining the pseudo-spectrum of the structured matrix we will derive estimates of the area of the approximate roots of the initial polynomial set. We will relate the strength of the GCD to the weighted strength of the pseudo-spectra and we investigate under which conditions the roots of the approximate GCDs are a subset of the pseudo-spectra.

Item Type: Article
Uncontrolled Keywords: Linear systems; approximate GCD; pseudo-spectrum; strength; algebraic computations
Subjects: Q Science > QA Mathematics
Divisions: School of Engineering & Mathematical Sciences > Engineering

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