An algorithm for locating all zeros of a real polynomial
Copyright policy )An algorithm for locating all zeros of a real polynomial
The authors present a globally convergent algorithm for calculating all zeros of a polynomial \(p_n\) with real coefficients. The calculation procedure starts with the stability test allowing to decide whether all zeros of \(p_n\) lie in the interior of the unit circle of the complex plane. It is also possible to get the exact number of zeros in the interior, on the boundary and in the exterior of a circle. Later the approximations of the zeros are calculated by appropriate iterative algorithms (e.g. Newton's or Bairstrow's type at the final stage).
- Rolf C. Hagen Group Canada
global convergence, Newton method, Bairstrow method, iterative algorithms, Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral), Computational aspects of field theory and polynomials, Numerical computation of solutions to single equations, stability test, Real polynomials: location of zeros, zeros of a real polynomial
global convergence, Newton method, Bairstrow method, iterative algorithms, Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral), Computational aspects of field theory and polynomials, Numerical computation of solutions to single equations, stability test, Real polynomials: location of zeros, zeros of a real polynomial
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