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On convergence of Nourein iterations for simultaneous finding all zeros of a polynomial. (English) Zbl 0953.65033

The authors study the zeros of polynomials and give the first estimation conditions for Nourein iterations for simultaneous finding all zeros of a polynomial. Futhermore the iteration processes are guaranteed to converge. An interesting numerical example is provided to illustrate the main results.

MSC:

65H05 Numerical computation of solutions to single equations
65Y05 Parallel numerical computation
12Y05 Computational aspects of field theory and polynomials (MSC2010)
26C10 Real polynomials: location of zeros
30C15 Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral)
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