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On the perturbation of the zeros of complex polynomials. (English) Zbl 0954.65037

The author investigates the deviation of the zeros of a polynomial and improves earlier results by A. Ostrowski [Solution of equations and systems of equations. (1960; Zbl 0115.11201), Appendix A] and A. Schönhage [The fundamental theorem of algebra in terms of computational complexity. Univ. Tübingen, preliminary report (1982)] by providing sharp estimate.The applications are given in estimating the differences of root-radii.

MSC:

65H05 Numerical computation of solutions to single equations
30C15 Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral)
65E05 General theory of numerical methods in complex analysis (potential theory, etc.)
12Y05 Computational aspects of field theory and polynomials (MSC2010)

Citations:

Zbl 0115.11201
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