Stability of Roots of Polynomials Under Linear Combinations of Derivatives |
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Authors: | Branko Ćurgus Vania Mascioni |
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Affiliation: | 1. Department of Mathematics, Western Washington University, Bellingham, WA, 98225, USA 2. Department of Mathematical Sciences, Ball State University, Muncie, IN, 47306-0490, USA
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Abstract: | Let T=α 0 I+α 1 D+⋅⋅⋅+α n D n , where D is the differentiation operator and a0 1 0alpha_{0}not=0 , and let f be a square-free polynomial with large minimum root separation. We prove that the roots of Tf are close to the roots of f translated by −α 1/α 0. |
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