Stability of Roots of Polynomials Under Linear Combinations of Derivatives |
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| Authors: | Branko Ćurgus Vania Mascioni |
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| Institution: | 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 0\alpha_{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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| Keywords: | |
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