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A hybrid method for polynomial complex zero. (English) Zbl 0724.65048

The paper deals with an iterative algorithm for finding isolated simple complex zeroes of a polynomial. Using Weierstrass’ interval formula for the simultaneous inclusion of all zeroes of the polynomial and rectangular floating-point arithmetic, a hybrid method with high computational efficiency is presented.
Furthermore, error bounds of the approximate solution are determined. In a second part, a computationally verifiable test for the existence of a zero in a given disc is established. A numerical example is given, too.
Reviewer: H.Kriete (Bochum)

MSC:

65H05 Numerical computation of solutions to single equations
65G30 Interval and finite arithmetic
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.)

Software:

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References:

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