Quadratic matrix polynomials with a parameter |
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Affiliation: | School of Mathematical Sciences, Tel Aviv University, Israel;Department of Mathematics and Statistics, University of Calgary, Canada;School of Mathematical Sciences, Tel Aviv University, Israel |
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Abstract: | In this paper we examine matrix polynomials of the form L(λ) = Aλ2 + εBλ + C in which ε is a parameter and A, B, C are positive definite. This arises in a natural way in the study of damped vibrating systems. The main results are concerned with the generic case in which det L(λ) has at least 2n − 1 distinct zeros for all ε ϵ [0, ∞). The values of ε at which there is a multiple zero of det L(λ) are of major interest in this analysis. The dependence of first degree factors of L(λ) on ε is also discussed. |
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