Abstract
Let T=α 0 I+α 1 D+⋅⋅⋅+α n D n, where D is the differentiation operator and \(\alpha_{0}\not=0\) , 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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Communicated by Edward B. Saff.
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Ćurgus, B., Mascioni, V. Stability of Roots of Polynomials Under Linear Combinations of Derivatives. Constr Approx 32, 523–541 (2010). https://doi.org/10.1007/s00365-009-9061-3
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DOI: https://doi.org/10.1007/s00365-009-9061-3